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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(10/54)-(15*(157/50)/60*(27/10))*7/(x+14)*(x+12)-4*asin(x+10)-1/sqrt(x+8)

¿Cómo vas a descomponer esta tan(10/54)-(15*(157/50)/60*(27/10))*7/(x+14)*(x+12)-4*asin(x+10)-1/sqrt(x+8) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
            /157*15\                                           
            |------|                                           
            \  50  /                                           
            --------*27                                        
               60                                              
            -----------*7                                      
                 10                                       1    
tan(5/27) - -------------*(x + 12) - 4*asin(x + 10) - ---------
                x + 14                                  _______
                                                      \/ x + 8
((−72715750⋅156010x+14(x+12)+tan⁡(527))−4asin⁡(x+10))−1x+8\left(\left(- \frac{7 \frac{27 \frac{\frac{157}{50} \cdot 15}{60}}{10}}{x + 14} \left(x + 12\right) + \tan{\left(\frac{5}{27} \right)}\right) - 4 \operatorname{asin}{\left(x + 10 \right)}\right) - \frac{1}{\sqrt{x + 8}} 
tan(5/27) - ((((157*15/50)/60)*27/10)*7)/(x + 14)*(x + 12) - 4*asin(x + 10) - 1/sqrt(x + 8)
Simplificación general [src] 
                  _______                                                            
          29673*\/ 8 + x *(12 + x)     _______                                       
-14 - x - ------------------------ + \/ 8 + x *(14 + x)*(-4*asin(10 + x) + tan(5/27))
                    2000                                                             
-------------------------------------------------------------------------------------
                                    _______                                          
                                  \/ 8 + x *(14 + x)
−x−29673x+8(x+12)2000+x+8(x+14)(−4asin⁡(x+10)+tan⁡(527))−14x+8(x+14)\frac{- x - \frac{29673 \sqrt{x + 8} \left(x + 12\right)}{2000} + \sqrt{x + 8} \left(x + 14\right) \left(- 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)}\right) - 14}{\sqrt{x + 8} \left(x + 14\right)} 
(-14 - x - 29673*sqrt(8 + x)*(12 + x)/2000 + sqrt(8 + x)*(14 + x)*(-4*asin(10 + x) + tan(5/27)))/(sqrt(8 + x)*(14 + x))
Potencias [src] 
      1                        29673*(12 + x)            
- --------- - 4*asin(10 + x) - -------------- + tan(5/27)
    _______                    2000*(14 + x)             
  \/ 8 + x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+tan⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} - \frac{1}{\sqrt{x + 8}} 
                                 89019   29673*x            
                               - ----- - -------            
      1                           500      2000             
- --------- - 4*asin(10 + x) + ----------------- + tan(5/27)
    _______                          14 + x                 
  \/ 8 + x
−29673x2000−89019500x+14−4asin⁡(x+10)+tan⁡(527)−1x+8\frac{- \frac{29673 x}{2000} - \frac{89019}{500}}{x + 14} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} - \frac{1}{\sqrt{x + 8}} 
                                                  /   5*I    -5*I\
                                                  |   ---    ----|
                                                  |    27     27 |
      1                        29673*(12 + x)   I*\- e    + e    /
- --------- - 4*asin(10 + x) - -------------- + ------------------
    _______                    2000*(14 + x)        -5*I    5*I   
  \/ 8 + x                                          ----    ---   
                                                     27      27   
                                                   e     + e
−29673(x+12)2000(x+14)−4asin⁡(x+10)+i(−e5i27+e−5i27)e−5i27+e5i27−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{i \left(- e^{\frac{5 i}{27}} + e^{- \frac{5 i}{27}}\right)}{e^{- \frac{5 i}{27}} + e^{\frac{5 i}{27}}} - \frac{1}{\sqrt{x + 8}} 
-1/sqrt(8 + x) - 4*asin(10 + x) - 29673*(12 + x)/(2000*(14 + x)) + i*(-exp(5*i/27) + exp(-5*i/27))/(exp(-5*i/27) + exp(5*i/27))
Unión de expresiones racionales [src] 
                    _______                                                                           
-28000 - 2000*x + \/ 8 + x *(-356076 - 29673*x - 8000*(14 + x)*asin(10 + x) + 2000*(14 + x)*tan(5/27))
------------------------------------------------------------------------------------------------------
                                              _______                                                 
                                       2000*\/ 8 + x *(14 + x)
−2000x+x+8(−29673x−8000(x+14)asin⁡(x+10)+2000(x+14)tan⁡(527)−356076)−280002000x+8(x+14)\frac{- 2000 x + \sqrt{x + 8} \left(- 29673 x - 8000 \left(x + 14\right) \operatorname{asin}{\left(x + 10 \right)} + 2000 \left(x + 14\right) \tan{\left(\frac{5}{27} \right)} - 356076\right) - 28000}{2000 \sqrt{x + 8} \left(x + 14\right)} 
(-28000 - 2000*x + sqrt(8 + x)*(-356076 - 29673*x - 8000*(14 + x)*asin(10 + x) + 2000*(14 + x)*tan(5/27)))/(2000*sqrt(8 + x)*(14 + x))
Denominador racional [src] 
                    _______                       _______                           _______            _______                        _______                          _______          
-420000 - 5341140*\/ 8 + x  - 30000*x - 1680000*\/ 8 + x *asin(10 + x) - 445095*x*\/ 8 + x  + 420000*\/ 8 + x *tan(5/27) - 120000*x*\/ 8 + x *asin(10 + x) + 30000*x*\/ 8 + x *tan(5/27)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                _______                                                                                                 
                                                                              \/ 8 + x *(420000 + 30000*x)
−120000xx+8asin⁡(x+10)−445095xx+8+30000xx+8tan⁡(527)−30000x−1680000x+8asin⁡(x+10)−5341140x+8+420000x+8tan⁡(527)−420000x+8(30000x+420000)\frac{- 120000 x \sqrt{x + 8} \operatorname{asin}{\left(x + 10 \right)} - 445095 x \sqrt{x + 8} + 30000 x \sqrt{x + 8} \tan{\left(\frac{5}{27} \right)} - 30000 x - 1680000 \sqrt{x + 8} \operatorname{asin}{\left(x + 10 \right)} - 5341140 \sqrt{x + 8} + 420000 \sqrt{x + 8} \tan{\left(\frac{5}{27} \right)} - 420000}{\sqrt{x + 8} \left(30000 x + 420000\right)} 
(-420000 - 5341140*sqrt(8 + x) - 30000*x - 1680000*sqrt(8 + x)*asin(10 + x) - 445095*x*sqrt(8 + x) + 420000*sqrt(8 + x)*tan(5/27) - 120000*x*sqrt(8 + x)*asin(10 + x) + 30000*x*sqrt(8 + x)*tan(5/27))/(sqrt(8 + x)*(420000 + 30000*x))
Abrimos la expresión [src] 
      1                           89019          29673*x               
- --------- - 4*asin(x + 10) - ------------ - ------------- + tan(5/27)
    _______                    500*(x + 14)   2000*(x + 14)            
  \/ x + 8
−29673x2000(x+14)−4asin⁡(x+10)+tan⁡(527)−89019500(x+14)−1x+8- \frac{29673 x}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} - \frac{89019}{500 \left(x + 14\right)} - \frac{1}{\sqrt{x + 8}} 
-1/sqrt(x + 8) - 4*asin(x + 10) - 89019/(500*(x + 14)) - 29673*x/(2000*(x + 14)) + tan(5/27)
Compilar la expresión [src] 
      1                        29673*(12 + x)            
- --------- - 4*asin(x + 10) - -------------- + tan(5/27)
    _______                    2000*(14 + x)             
  \/ 8 + x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+tan⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} - \frac{1}{\sqrt{x + 8}} 
-1/sqrt(8 + x) - 4*asin(x + 10) - 29673*(12 + x)/(2000*(14 + x)) + tan(5/27)
Respuesta numérica [src] 
0.187331518129431 - 4.0*asin(x + 10) - 0.353553390593274*(1 + 0.125*x)^(-0.5) - 14.8365*(12.0 + x)/(14.0 + x)
0.187331518129431 - 4.0*asin(x + 10) - 0.353553390593274*(1 + 0.125*x)^(-0.5) - 14.8365*(12.0 + x)/(14.0 + x)
Combinatoria [src] 
 /                          _______           _______                       _______            _______                         _______                      _______             \ 
-\28000 + 2000*x + 356076*\/ 8 + x  - 28000*\/ 8 + x *tan(5/27) + 29673*x*\/ 8 + x  + 112000*\/ 8 + x *asin(10 + x) - 2000*x*\/ 8 + x *tan(5/27) + 8000*x*\/ 8 + x *asin(10 + x)/ 
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                    _______                                                                                       
                                                                             2000*\/ 8 + x *(14 + x)
−8000xx+8asin⁡(x+10)−2000xx+8tan⁡(527)+29673xx+8+2000x+112000x+8asin⁡(x+10)−28000x+8tan⁡(527)+356076x+8+280002000x+8(x+14)- \frac{8000 x \sqrt{x + 8} \operatorname{asin}{\left(x + 10 \right)} - 2000 x \sqrt{x + 8} \tan{\left(\frac{5}{27} \right)} + 29673 x \sqrt{x + 8} + 2000 x + 112000 \sqrt{x + 8} \operatorname{asin}{\left(x + 10 \right)} - 28000 \sqrt{x + 8} \tan{\left(\frac{5}{27} \right)} + 356076 \sqrt{x + 8} + 28000}{2000 \sqrt{x + 8} \left(x + 14\right)} 
-(28000 + 2000*x + 356076*sqrt(8 + x) - 28000*sqrt(8 + x)*tan(5/27) + 29673*x*sqrt(8 + x) + 112000*sqrt(8 + x)*asin(10 + x) - 2000*x*sqrt(8 + x)*tan(5/27) + 8000*x*sqrt(8 + x)*asin(10 + x))/(2000*sqrt(8 + x)*(14 + x))
Denominador común [src] 
                                            _______                      
  29673                     14000 - 29673*\/ 8 + x  + 1000*x             
- ----- - 4*asin(10 + x) - ---------------------------------- + tan(5/27)
   2000                            _______            _______            
                           14000*\/ 8 + x  + 1000*x*\/ 8 + x
−4asin⁡(x+10)−296732000+tan⁡(527)−1000x−29673x+8+140001000xx+8+14000x+8- 4 \operatorname{asin}{\left(x + 10 \right)} - \frac{29673}{2000} + \tan{\left(\frac{5}{27} \right)} - \frac{1000 x - 29673 \sqrt{x + 8} + 14000}{1000 x \sqrt{x + 8} + 14000 \sqrt{x + 8}} 
-29673/2000 - 4*asin(10 + x) - (14000 - 29673*sqrt(8 + x) + 1000*x)/(14000*sqrt(8 + x) + 1000*x*sqrt(8 + x)) + tan(5/27)
Parte trigonométrica [src] 
                                  /  5    pi\                 
                               csc|- -- + --|                 
      1                           \  27   2 /   29673*(12 + x)
- --------- - 4*asin(10 + x) + -------------- - --------------
    _______                      csc(5/27)      2000*(14 + x) 
  \/ 8 + x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+csc⁡(−527+π2)csc⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\csc{\left(- \frac{5}{27} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}} 
      1                        sin(5/27)   29673*(12 + x)
- --------- - 4*asin(10 + x) + --------- - --------------
    _______                    cos(5/27)   2000*(14 + x) 
  \/ 8 + x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+sin⁡(527)cos⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\sin{\left(\frac{5}{27} \right)}}{\cos{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}} 
                                    /10   pi\                 
                               2*sec|-- - --|                 
      1                             \27   2 /   29673*(12 + x)
- --------- - 4*asin(10 + x) + -------------- - --------------
    _______                       2/5    pi\    2000*(14 + x) 
  \/ 8 + x                     sec |-- - --|                  
                                   \27   2 /
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2sec⁡(1027−π2)sec⁡2(527−π2)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \sec{\left(\frac{10}{27} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{5}{27} - \frac{\pi}{2} \right)}} - \frac{1}{\sqrt{x + 8}} 
      1                         sec(5/27)     29673*(12 + x)
- --------- - 4*asin(10 + x) + ------------ - --------------
    _______                       /5    pi\   2000*(14 + x) 
  \/ 8 + x                     sec|-- - --|                 
                                  \27   2 /
−29673(x+12)2000(x+14)−4asin⁡(x+10)+sec⁡(527)sec⁡(527−π2)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\sec{\left(\frac{5}{27} \right)}}{\sec{\left(\frac{5}{27} - \frac{\pi}{2} \right)}} - \frac{1}{\sqrt{x + 8}} 
      1                        29673*(12 + x)            
- --------- - 4*asin(10 + x) - -------------- + tan(5/27)
    _______                    2000*(14 + x)             
  \/ 8 + x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+tan⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} - \frac{1}{\sqrt{x + 8}} 
                                                     2       /    1                \
                                                4*tan (5/54)*|--------- + tan(5/27)|
      1                        29673*(12 + x)                \tan(5/27)            /
- --------- - 4*asin(10 + x) - -------------- + ------------------------------------
    _______                    2000*(14 + x)                             2          
  \/ 8 + x                                               /       2      \           
                                                         \1 + tan (5/54)/
−29673(x+12)2000(x+14)−4asin⁡(x+10)+4(tan⁡(527)+1tan⁡(527))tan⁡2(554)(tan⁡2(554)+1)2−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{4 \left(\tan{\left(\frac{5}{27} \right)} + \frac{1}{\tan{\left(\frac{5}{27} \right)}}\right) \tan^{2}{\left(\frac{5}{54} \right)}}{\left(\tan^{2}{\left(\frac{5}{54} \right)} + 1\right)^{2}} - \frac{1}{\sqrt{x + 8}} 
      1                             2          /10\   29673*(12 + x)
- --------- - 4*asin(10 + x) + 2*sin (5/27)*csc|--| - --------------
    _______                                    \27/   2000*(14 + x) 
  \/ 8 + x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2sin⁡2(527)csc⁡(1027)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + 2 \sin^{2}{\left(\frac{5}{27} \right)} \csc{\left(\frac{10}{27} \right)} - \frac{1}{\sqrt{x + 8}} 
                                    2                       
      1                        2*sin (5/27)   29673*(12 + x)
- --------- - 4*asin(10 + x) + ------------ - --------------
    _______                         /10\      2000*(14 + x) 
  \/ 8 + x                       sin|--|                    
                                    \27/
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2sin⁡2(527)sin⁡(1027)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \sin^{2}{\left(\frac{5}{27} \right)}}{\sin{\left(\frac{10}{27} \right)}} - \frac{1}{\sqrt{x + 8}} 
                                  /5    pi\                 
                               cos|-- - --|                 
      1                           \27   2 /   29673*(12 + x)
- --------- - 4*asin(10 + x) + ------------ - --------------
    _______                     cos(5/27)     2000*(14 + x) 
  \/ 8 + x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+cos⁡(527−π2)cos⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\cos{\left(\frac{5}{27} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}} 
    1           1                        29673*(12 + x)
--------- - --------- - 4*asin(10 + x) - --------------
cot(5/27)     _______                    2000*(14 + x) 
            \/ 8 + x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+1cot⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{1}{\cot{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}} 
                                                     2       /       2      \
      1                        29673*(12 + x)   4*tan (5/54)*\1 + tan (5/27)/
- --------- - 4*asin(10 + x) - -------------- + -----------------------------
    _______                    2000*(14 + x)                     2           
  \/ 8 + x                                       /       2      \            
                                                 \1 + tan (5/54)/ *tan(5/27)
−29673(x+12)2000(x+14)−4asin⁡(x+10)+4(tan⁡2(527)+1)tan⁡2(554)(tan⁡2(554)+1)2tan⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{4 \left(\tan^{2}{\left(\frac{5}{27} \right)} + 1\right) \tan^{2}{\left(\frac{5}{54} \right)}}{\left(\tan^{2}{\left(\frac{5}{54} \right)} + 1\right)^{2} \tan{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}} 
                                    /10\                  
                               2*csc|--|                  
      1                             \27/    29673*(12 + x)
- --------- - 4*asin(10 + x) + ---------- - --------------
    _______                       2         2000*(14 + x) 
  \/ 8 + x                     csc (5/27)
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2csc⁡(1027)csc⁡2(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \csc{\left(\frac{10}{27} \right)}}{\csc^{2}{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}} 
                                                     2       /       2      \
      1                        29673*(12 + x)   4*cot (5/54)*\1 + cot (5/27)/
- --------- - 4*asin(10 + x) - -------------- + -----------------------------
    _______                    2000*(14 + x)                     2           
  \/ 8 + x                                       /       2      \            
                                                 \1 + cot (5/54)/ *cot(5/27)
−29673(x+12)2000(x+14)−4asin⁡(x+10)+4(1+cot⁡2(527))cot⁡2(554)(1+cot⁡2(554))2cot⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{4 \left(1 + \cot^{2}{\left(\frac{5}{27} \right)}\right) \cot^{2}{\left(\frac{5}{54} \right)}}{\left(1 + \cot^{2}{\left(\frac{5}{54} \right)}\right)^{2} \cot{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}} 
                                    2/5    pi\                 
                               2*cos |-- - --|                 
      1                              \27   2 /   29673*(12 + x)
- --------- - 4*asin(10 + x) + --------------- - --------------
    _______                         /10   pi\    2000*(14 + x) 
  \/ 8 + x                       cos|-- - --|                  
                                    \27   2 /
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2cos⁡2(527−π2)cos⁡(1027−π2)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \cos^{2}{\left(\frac{5}{27} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{10}{27} - \frac{\pi}{2} \right)}} - \frac{1}{\sqrt{x + 8}} 
      1                        sec(5/27)   29673*(12 + x)
- --------- - 4*asin(10 + x) + --------- - --------------
    _______                    csc(5/27)   2000*(14 + x) 
  \/ 8 + x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+sec⁡(527)csc⁡(527)−1x+8- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\sec{\left(\frac{5}{27} \right)}}{\csc{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}} 
-1/sqrt(8 + x) - 4*asin(10 + x) + sec(5/27)/csc(5/27) - 29673*(12 + x)/(2000*(14 + x))
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