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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) - ----- + 8
                x + 14                                  ___    
                                                      \/ x
(((−72715750⋅156010x+14(x+12)+tan⁡(527))−4asin⁡(x+10))−1x)+8\left(\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}}\right) + 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*\/ x *(12 + x)     ___                                          
-14 - x - -------------------- + \/ x *(14 + x)*(8 - 4*asin(10 + x) + tan(5/27))
                  2000                                                          
--------------------------------------------------------------------------------
                                   ___                                          
                                 \/ x *(14 + x)
−29673x(x+12)2000+x(x+14)(−4asin⁡(x+10)+tan⁡(527)+8)−x−14x(x+14)\frac{- \frac{29673 \sqrt{x} \left(x + 12\right)}{2000} + \sqrt{x} \left(x + 14\right) \left(- 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8\right) - x - 14}{\sqrt{x} \left(x + 14\right)} 
(-14 - x - 29673*sqrt(x)*(12 + x)/2000 + sqrt(x)*(14 + x)*(8 - 4*asin(10 + x) + tan(5/27)))/(sqrt(x)*(14 + x))
Respuesta numérica [src] 
8.18733151812943 - x^(-0.5) - 4.0*asin(x + 10) - 14.8365*(12.0 + x)/(14.0 + x)
8.18733151812943 - x^(-0.5) - 4.0*asin(x + 10) - 14.8365*(12.0 + x)/(14.0 + x)
Unión de expresiones racionales [src] 
                    ___                                                                                      ___         
-28000 - 2000*x + \/ x *(-356076 - 29673*x - 8000*(14 + x)*asin(10 + x) + 2000*(14 + x)*tan(5/27)) + 16000*\/ x *(14 + x)
-------------------------------------------------------------------------------------------------------------------------
                                                          ___                                                            
                                                   2000*\/ x *(14 + x)
16000x(x+14)+x(−29673x−8000(x+14)asin⁡(x+10)+2000(x+14)tan⁡(527)−356076)−2000x−280002000x(x+14)\frac{16000 \sqrt{x} \left(x + 14\right) + \sqrt{x} \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) - 2000 x - 28000}{2000 \sqrt{x} \left(x + 14\right)} 
(-28000 - 2000*x + sqrt(x)*(-356076 - 29673*x - 8000*(14 + x)*asin(10 + x) + 2000*(14 + x)*tan(5/27)) + 16000*sqrt(x)*(14 + x))/(2000*sqrt(x)*(14 + x))
Potencias [src] 
      1                      29673*(12 + x)            
8 - ----- - 4*asin(10 + x) - -------------- + tan(5/27)
      ___                    2000*(14 + x)             
    \/ x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+tan⁡(527)+8−1x- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8 - \frac{1}{\sqrt{x}} 
                                                /   5*I    -5*I\
                                                |   ---    ----|
                                                |    27     27 |
      1                      29673*(12 + x)   I*\- e    + e    /
8 - ----- - 4*asin(10 + x) - -------------- + ------------------
      ___                    2000*(14 + x)        -5*I    5*I   
    \/ x                                          ----    ---   
                                                   27      27   
                                                 e     + e
−29673(x+12)2000(x+14)−4asin⁡(x+10)+8+i(−e5i27+e−5i27)e−5i27+e5i27−1x- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + 8 + \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}} 
                               89019   29673*x            
                             - ----- - -------            
      1                         500      2000             
8 - ----- - 4*asin(10 + x) + ----------------- + tan(5/27)
      ___                          14 + x                 
    \/ x
−29673x2000−89019500x+14−4asin⁡(x+10)+tan⁡(527)+8−1x\frac{- \frac{29673 x}{2000} - \frac{89019}{500}}{x + 14} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8 - \frac{1}{\sqrt{x}} 
8 - 1/sqrt(x) - 4*asin(10 + x) + (-89019/500 - 29673*x/2000)/(14 + x) + tan(5/27)
Combinatoria [src] 
 /                        3/2            ___           ___                   3/2                   3/2                         ___             \ 
-\28000 + 2000*x + 13673*x    + 132076*\/ x  - 28000*\/ x *tan(5/27) - 2000*x   *tan(5/27) + 8000*x   *asin(10 + x) + 112000*\/ x *asin(10 + x)/ 
-------------------------------------------------------------------------------------------------------------------------------------------------
                                                                      ___                                                                        
                                                               2000*\/ x *(14 + x)
−8000x32asin⁡(x+10)−2000x32tan⁡(527)+13673x32+112000xasin⁡(x+10)−28000xtan⁡(527)+132076x+2000x+280002000x(x+14)- \frac{8000 x^{\frac{3}{2}} \operatorname{asin}{\left(x + 10 \right)} - 2000 x^{\frac{3}{2}} \tan{\left(\frac{5}{27} \right)} + 13673 x^{\frac{3}{2}} + 112000 \sqrt{x} \operatorname{asin}{\left(x + 10 \right)} - 28000 \sqrt{x} \tan{\left(\frac{5}{27} \right)} + 132076 \sqrt{x} + 2000 x + 28000}{2000 \sqrt{x} \left(x + 14\right)} 
-(28000 + 2000*x + 13673*x^(3/2) + 132076*sqrt(x) - 28000*sqrt(x)*tan(5/27) - 2000*x^(3/2)*tan(5/27) + 8000*x^(3/2)*asin(10 + x) + 112000*sqrt(x)*asin(10 + x))/(2000*sqrt(x)*(14 + x))
Denominador común [src] 
                                           ___                     
  13673                    14000 - 29673*\/ x  + 1000*x            
- ----- - 4*asin(10 + x) - ---------------------------- + tan(5/27)
   2000                            3/2           ___               
                             1000*x    + 14000*\/ x
−4asin⁡(x+10)−136732000+tan⁡(527)−−29673x+1000x+140001000x32+14000x- 4 \operatorname{asin}{\left(x + 10 \right)} - \frac{13673}{2000} + \tan{\left(\frac{5}{27} \right)} - \frac{- 29673 \sqrt{x} + 1000 x + 14000}{1000 x^{\frac{3}{2}} + 14000 \sqrt{x}} 
-13673/2000 - 4*asin(10 + x) - (14000 - 29673*sqrt(x) + 1000*x)/(1000*x^(3/2) + 14000*sqrt(x)) + tan(5/27)
Denominador racional [src] 
                    ___           3/2                       ___                        3/2                       3/2                      ___          
-420000 - 1981140*\/ x  - 205095*x    - 30000*x - 1680000*\/ x *asin(10 + x) - 120000*x   *asin(10 + x) + 30000*x   *tan(5/27) + 420000*\/ x *tan(5/27)
-------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                  ___                                                                                  
                                                                \/ x *(420000 + 30000*x)
−120000x32asin⁡(x+10)−205095x32+30000x32tan⁡(527)−1680000xasin⁡(x+10)−1981140x+420000xtan⁡(527)−30000x−420000x(30000x+420000)\frac{- 120000 x^{\frac{3}{2}} \operatorname{asin}{\left(x + 10 \right)} - 205095 x^{\frac{3}{2}} + 30000 x^{\frac{3}{2}} \tan{\left(\frac{5}{27} \right)} - 1680000 \sqrt{x} \operatorname{asin}{\left(x + 10 \right)} - 1981140 \sqrt{x} + 420000 \sqrt{x} \tan{\left(\frac{5}{27} \right)} - 30000 x - 420000}{\sqrt{x} \left(30000 x + 420000\right)} 
(-420000 - 1981140*sqrt(x) - 205095*x^(3/2) - 30000*x - 1680000*sqrt(x)*asin(10 + x) - 120000*x^(3/2)*asin(10 + x) + 30000*x^(3/2)*tan(5/27) + 420000*sqrt(x)*tan(5/27))/(sqrt(x)*(420000 + 30000*x))
Abrimos la expresión [src] 
      1                         89019          29673*x               
8 - ----- - 4*asin(x + 10) - ------------ - ------------- + tan(5/27)
      ___                    500*(x + 14)   2000*(x + 14)            
    \/ x
−29673x2000(x+14)−4asin⁡(x+10)+tan⁡(527)+8−89019500(x+14)−1x- \frac{29673 x}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8 - \frac{89019}{500 \left(x + 14\right)} - \frac{1}{\sqrt{x}} 
8 - 1/sqrt(x) - 4*asin(x + 10) - 89019/(500*(x + 14)) - 29673*x/(2000*(x + 14)) + tan(5/27)
Compilar la expresión [src] 
      1                      29673*(12 + x)            
8 - ----- - 4*asin(x + 10) - -------------- + tan(5/27)
      ___                    2000*(14 + x)             
    \/ x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+tan⁡(527)+8−1x- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8 - \frac{1}{\sqrt{x}} 
8 - 1/sqrt(x) - 4*asin(x + 10) - 29673*(12 + x)/(2000*(14 + x)) + tan(5/27)
Parte trigonométrica [src] 
      1                      29673*(12 + x)            
8 - ----- - 4*asin(10 + x) - -------------- + tan(5/27)
      ___                    2000*(14 + x)             
    \/ x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+tan⁡(527)+8−1x- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8 - \frac{1}{\sqrt{x}} 
                                /  5    pi\                 
                             csc|- -- + --|                 
      1                         \  27   2 /   29673*(12 + x)
8 - ----- - 4*asin(10 + x) + -------------- - --------------
      ___                      csc(5/27)      2000*(14 + x) 
    \/ x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+csc⁡(−527+π2)csc⁡(527)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
                                  2/5    pi\                 
                             2*cos |-- - --|                 
      1                            \27   2 /   29673*(12 + x)
8 - ----- - 4*asin(10 + x) + --------------- - --------------
      ___                         /10   pi\    2000*(14 + x) 
    \/ x                       cos|-- - --|                  
                                  \27   2 /
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2cos⁡2(527−π2)cos⁡(1027−π2)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
      1                       sec(5/27)     29673*(12 + x)
8 - ----- - 4*asin(10 + x) + ------------ - --------------
      ___                       /5    pi\   2000*(14 + x) 
    \/ x                     sec|-- - --|                 
                                \27   2 /
−29673(x+12)2000(x+14)−4asin⁡(x+10)+sec⁡(527)sec⁡(527−π2)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
                                  2                       
      1                      2*sin (5/27)   29673*(12 + x)
8 - ----- - 4*asin(10 + x) + ------------ - --------------
      ___                         /10\      2000*(14 + x) 
    \/ x                       sin|--|                    
                                  \27/
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2sin⁡2(527)sin⁡(1027)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
      1                      sec(5/27)   29673*(12 + x)
8 - ----- - 4*asin(10 + x) + --------- - --------------
      ___                    csc(5/27)   2000*(14 + x) 
    \/ x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+sec⁡(527)csc⁡(527)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
                                                   2       /       2      \
      1                      29673*(12 + x)   4*tan (5/54)*\1 + tan (5/27)/
8 - ----- - 4*asin(10 + x) - -------------- + -----------------------------
      ___                    2000*(14 + x)                     2           
    \/ 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)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
      1                      sin(5/27)   29673*(12 + x)
8 - ----- - 4*asin(10 + x) + --------- - --------------
      ___                    cos(5/27)   2000*(14 + x) 
    \/ x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+sin⁡(527)cos⁡(527)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
                                  /10   pi\                 
                             2*sec|-- - --|                 
      1                           \27   2 /   29673*(12 + x)
8 - ----- - 4*asin(10 + x) + -------------- - --------------
      ___                       2/5    pi\    2000*(14 + x) 
    \/ x                     sec |-- - --|                  
                                 \27   2 /
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2sec⁡(1027−π2)sec⁡2(527−π2)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
      1                           2          /10\   29673*(12 + x)
8 - ----- - 4*asin(10 + x) + 2*sin (5/27)*csc|--| - --------------
      ___                                    \27/   2000*(14 + x) 
    \/ x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2sin⁡2(527)csc⁡(1027)+8−1x- \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)} + 8 - \frac{1}{\sqrt{x}} 
        1         1                      29673*(12 + x)
8 + --------- - ----- - 4*asin(10 + x) - --------------
    cot(5/27)     ___                    2000*(14 + x) 
                \/ x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+1cot⁡(527)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
                                  /10\                  
                             2*csc|--|                  
      1                           \27/    29673*(12 + x)
8 - ----- - 4*asin(10 + x) + ---------- - --------------
      ___                       2         2000*(14 + x) 
    \/ x                     csc (5/27)
−29673(x+12)2000(x+14)−4asin⁡(x+10)+2csc⁡(1027)csc⁡2(527)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
                                                   2       /       2      \
      1                      29673*(12 + x)   4*cot (5/54)*\1 + cot (5/27)/
8 - ----- - 4*asin(10 + x) - -------------- + -----------------------------
      ___                    2000*(14 + x)                     2           
    \/ 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)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
                                /5    pi\                 
                             cos|-- - --|                 
      1                         \27   2 /   29673*(12 + x)
8 - ----- - 4*asin(10 + x) + ------------ - --------------
      ___                     cos(5/27)     2000*(14 + x) 
    \/ x
−29673(x+12)2000(x+14)−4asin⁡(x+10)+cos⁡(527−π2)cos⁡(527)+8−1x- \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)}} + 8 - \frac{1}{\sqrt{x}} 
                                                   2       /    1                \
                                              4*tan (5/54)*|--------- + tan(5/27)|
      1                      29673*(12 + x)                \tan(5/27)            /
8 - ----- - 4*asin(10 + x) - -------------- + ------------------------------------
      ___                    2000*(14 + x)                             2          
    \/ 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+8−1x- \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}} + 8 - \frac{1}{\sqrt{x}} 
8 - 1/sqrt(x) - 4*asin(10 + x) - 29673*(12 + x)/(2000*(14 + x)) + 4*tan(5/54)^2*(1/tan(5/27) + tan(5/27))/(1 + tan(5/54)^2)^2
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