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¿Cómo vas a descomponer esta (4*x^5)/5+2*x^4+(2*x^3)/3-x^2-3/(2*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
   5             3            
4*x       4   2*x     2    3  
---- + 2*x  + ---- - x  - ----
 5             3             2
                          2*x 
(x2+(2x33+(2x4+4x55)))32x2\left(- x^{2} + \left(\frac{2 x^{3}}{3} + \left(2 x^{4} + \frac{4 x^{5}}{5}\right)\right)\right) - \frac{3}{2 x^{2}}
(4*x^5)/5 + 2*x^4 + (2*x^3)/3 - x^2 - 3*1/(2*x^2)
Descomposición de una fracción [src]
-x^2 + 2*x^4 - 3/(2*x^2) + 2*x^3/3 + 4*x^5/5
4x55+2x4+2x33x232x2\frac{4 x^{5}}{5} + 2 x^{4} + \frac{2 x^{3}}{3} - x^{2} - \frac{3}{2 x^{2}}
                        3      5
   2      4    3     2*x    4*x 
- x  + 2*x  - ---- + ---- + ----
                 2    3      5  
              2*x               
Simplificación general [src]
         4 /                 3       2\
-45 + 2*x *\-15 + 10*x + 12*x  + 30*x /
---------------------------------------
                     2                 
                 30*x                  
2x4(12x3+30x2+10x15)4530x2\frac{2 x^{4} \left(12 x^{3} + 30 x^{2} + 10 x - 15\right) - 45}{30 x^{2}}
(-45 + 2*x^4*(-15 + 10*x + 12*x^3 + 30*x^2))/(30*x^2)
Respuesta numérica [src]
-x^2 + 2.0*x^4 + 0.8*x^5 + 0.666666666666667*x^3 - 1.5/x^2
-x^2 + 2.0*x^4 + 0.8*x^5 + 0.666666666666667*x^3 - 1.5/x^2
Compilar la expresión [src]
                        3      5
   2      4    3     2*x    4*x 
- x  + 2*x  - ---- + ---- + ----
                 2    3      5  
              2*x               
4x55+2x4+2x33x232x2\frac{4 x^{5}}{5} + 2 x^{4} + \frac{2 x^{3}}{3} - x^{2} - \frac{3}{2 x^{2}}
-x^2 + 2*x^4 - 3/(2*x^2) + 2*x^3/3 + 4*x^5/5
Denominador racional [src]
         2 /      2       3       5       4\
-45 + 2*x *\- 15*x  + 10*x  + 12*x  + 30*x /
--------------------------------------------
                       2                    
                   30*x                     
2x2(12x5+30x4+10x315x2)4530x2\frac{2 x^{2} \left(12 x^{5} + 30 x^{4} + 10 x^{3} - 15 x^{2}\right) - 45}{30 x^{2}}
(-45 + 2*x^2*(-15*x^2 + 10*x^3 + 12*x^5 + 30*x^4))/(30*x^2)
Abrimos la expresión [src]
                        3      5
   2      4    3     2*x    4*x 
- x  + 2*x  - ---- + ---- + ----
                 2    3      5  
              2*x               
2x4x2+2x33+4x5532x22 x^{4} - x^{2} + \frac{2 x^{3}}{3} + \frac{4 x^{5}}{5} - \frac{3}{2 x^{2}}
-x^2 + 2*x^4 - 3/(2*x^2) + (2*x^3)/3 + (4*x^5)/5
Parte trigonométrica [src]
                        3      5
   2      4    3     2*x    4*x 
- x  + 2*x  - ---- + ---- + ----
                 2    3      5  
              2*x               
4x55+2x4+2x33x232x2\frac{4 x^{5}}{5} + 2 x^{4} + \frac{2 x^{3}}{3} - x^{2} - \frac{3}{2 x^{2}}
-x^2 + 2*x^4 - 3/(2*x^2) + 2*x^3/3 + 4*x^5/5
Denominador común [src]
                        3      5
   2      4    3     2*x    4*x 
- x  + 2*x  - ---- + ---- + ----
                 2    3      5  
              2*x               
4x55+2x4+2x33x232x2\frac{4 x^{5}}{5} + 2 x^{4} + \frac{2 x^{3}}{3} - x^{2} - \frac{3}{2 x^{2}}
-x^2 + 2*x^4 - 3/(2*x^2) + 2*x^3/3 + 4*x^5/5
Potencias [src]
                        3      5
   2      4    3     2*x    4*x 
- x  + 2*x  - ---- + ---- + ----
                 2    3      5  
              2*x               
4x55+2x4+2x33x232x2\frac{4 x^{5}}{5} + 2 x^{4} + \frac{2 x^{3}}{3} - x^{2} - \frac{3}{2 x^{2}}
-x^2 + 2*x^4 - 3/(2*x^2) + 2*x^3/3 + 4*x^5/5
Combinatoria [src]
          4       5       7       6
-45 - 30*x  + 20*x  + 24*x  + 60*x 
-----------------------------------
                   2               
               30*x                
24x7+60x6+20x530x44530x2\frac{24 x^{7} + 60 x^{6} + 20 x^{5} - 30 x^{4} - 45}{30 x^{2}}
(-45 - 30*x^4 + 20*x^5 + 24*x^7 + 60*x^6)/(30*x^2)
Unión de expresiones racionales [src]
         4                                
-45 + 2*x *(-15 + 2*x*(5 + 3*x*(5 + 2*x)))
------------------------------------------
                      2                   
                  30*x                    
2x4(2x(3x(2x+5)+5)15)4530x2\frac{2 x^{4} \left(2 x \left(3 x \left(2 x + 5\right) + 5\right) - 15\right) - 45}{30 x^{2}}
(-45 + 2*x^4*(-15 + 2*x*(5 + 3*x*(5 + 2*x))))/(30*x^2)