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¿Cómo vas a descomponer esta ((x+1)^2*(8*x-4))^(1/3)*(8*(x+1)^2/3+(2+2*x)*(8*x-4)/3)/((x+1)^2*(8*x-4)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
   ____________________ /         2                      \
3 /        2            |8*(x + 1)    (2 + 2*x)*(8*x - 4)|
\/  (x + 1) *(8*x - 4) *|---------- + -------------------|
                        \    3                 3         /
----------------------------------------------------------
                           2                              
                    (x + 1) *(8*x - 4)                    
$$\frac{\sqrt[3]{\left(x + 1\right)^{2} \left(8 x - 4\right)} \left(\frac{\left(2 x + 2\right) \left(8 x - 4\right)}{3} + \frac{8 \left(x + 1\right)^{2}}{3}\right)}{\left(x + 1\right)^{2} \left(8 x - 4\right)}$$
(((x + 1)^2*(8*x - 4))^(1/3)*((8*(x + 1)^2)/3 + ((2 + 2*x)*(8*x - 4))/3))/(((x + 1)^2*(8*x - 4)))
Simplificación general [src]
            _____________________
     2/3 3 /        2            
2*x*2   *\/  (1 + x) *(-1 + 2*x) 
---------------------------------
        (1 + x)*(-1 + 2*x)       
$$\frac{2 \cdot 2^{\frac{2}{3}} x \sqrt[3]{\left(x + 1\right)^{2} \left(2 x - 1\right)}}{\left(x + 1\right) \left(2 x - 1\right)}$$
2*x*2^(2/3)*((1 + x)^2*(-1 + 2*x))^(1/3)/((1 + x)*(-1 + 2*x))
Denominador racional [src]
   _____________________                                    
3 /        2             /         2                       \
\/  (1 + x) *(-4 + 8*x) *\8*(1 + x)  + (-4 + 8*x)*(2 + 2*x)/
------------------------------------------------------------
                            2                               
                   3*(1 + x) *(-4 + 8*x)                    
$$\frac{\sqrt[3]{\left(x + 1\right)^{2} \left(8 x - 4\right)} \left(8 \left(x + 1\right)^{2} + \left(2 x + 2\right) \left(8 x - 4\right)\right)}{3 \left(x + 1\right)^{2} \left(8 x - 4\right)}$$
((1 + x)^2*(-4 + 8*x))^(1/3)*(8*(1 + x)^2 + (-4 + 8*x)*(2 + 2*x))/(3*(1 + x)^2*(-4 + 8*x))
Abrimos la expresión [src]
   __________ /         2                      \
3 /        2  |8*(x + 1)    (2 + 2*x)*(8*x - 4)|
\/  (x + 1)  *|---------- + -------------------|
              \    3                 3         /
------------------------------------------------
                    2          2/3              
             (x + 1) *(8*x - 4)                 
$$\frac{\left(\frac{\left(2 x + 2\right) \left(8 x - 4\right)}{3} + \frac{8 \left(x + 1\right)^{2}}{3}\right) \sqrt[3]{\left(x + 1\right)^{2}}}{\left(x + 1\right)^{2} \left(8 x - 4\right)^{\frac{2}{3}}}$$
((x + 1)^2)^(1/3)*((8*(x + 1)^2)/3 + ((2 + 2*x)*(8*x - 4))/3)/((x + 1)^2*(8*x - 4)^(2/3))
Parte trigonométrica [src]
   _____________________ /         2                       \
3 /        2             |8*(1 + x)    (-4 + 8*x)*(2 + 2*x)|
\/  (1 + x) *(-4 + 8*x) *|---------- + --------------------|
                         \    3                 3          /
------------------------------------------------------------
                           2                                
                    (1 + x) *(-4 + 8*x)                     
$$\frac{\sqrt[3]{\left(x + 1\right)^{2} \left(8 x - 4\right)} \left(\frac{8 \left(x + 1\right)^{2}}{3} + \frac{\left(2 x + 2\right) \left(8 x - 4\right)}{3}\right)}{\left(x + 1\right)^{2} \left(8 x - 4\right)}$$
((1 + x)^2*(-4 + 8*x))^(1/3)*(8*(1 + x)^2/3 + (-4 + 8*x)*(2 + 2*x)/3)/((1 + x)^2*(-4 + 8*x))
Respuesta numérica [src]
((1.0 + x)^2*(-4.0 + 8.0*x))^0.333333333333333*(2.66666666666667*(1.0 + x)^2 + 0.333333333333333*(2.0 + 2.0*x)*(-4.0 + 8.0*x))/((1.0 + x)^2*(-4.0 + 8.0*x))
((1.0 + x)^2*(-4.0 + 8.0*x))^0.333333333333333*(2.66666666666667*(1.0 + x)^2 + 0.333333333333333*(2.0 + 2.0*x)*(-4.0 + 8.0*x))/((1.0 + x)^2*(-4.0 + 8.0*x))
Compilar la expresión [src]
   _____________________ /         2                       \
3 /        2             |8*(1 + x)    (-4 + 8*x)*(2 + 2*x)|
\/  (1 + x) *(-4 + 8*x) *|---------- + --------------------|
                         \    3                 3          /
------------------------------------------------------------
                           2                                
                    (1 + x) *(-4 + 8*x)                     
$$\frac{\sqrt[3]{\left(x + 1\right)^{2} \left(8 x - 4\right)} \left(\frac{8 \left(x + 1\right)^{2}}{3} + \frac{\left(2 x + 2\right) \left(8 x - 4\right)}{3}\right)}{\left(x + 1\right)^{2} \left(8 x - 4\right)}$$
((1 + x)^2*(-4 + 8*x))^(1/3)*(8*(1 + x)^2/3 + (-4 + 8*x)*(2 + 2*x)/3)/((1 + x)^2*(-4 + 8*x))
Unión de expresiones racionales [src]
            _____________________          
     2/3 3 /        2             /8   8*x\
3*x*2   *\/  (1 + x) *(-1 + 2*x) *|- + ---|
                                  \3    3 /
-------------------------------------------
                    2                      
           4*(1 + x) *(-1 + 2*x)           
$$\frac{3 \cdot 2^{\frac{2}{3}} x \sqrt[3]{\left(x + 1\right)^{2} \left(2 x - 1\right)} \left(\frac{8 x}{3} + \frac{8}{3}\right)}{4 \left(x + 1\right)^{2} \left(2 x - 1\right)}$$
3*x*2^(2/3)*((1 + x)^2*(-1 + 2*x))^(1/3)*(8/3 + 8*x/3)/(4*(1 + x)^2*(-1 + 2*x))
Potencias [src]
   _____________________ /         2                       \
3 /        2             |8*(1 + x)    (-4 + 8*x)*(2 + 2*x)|
\/  (1 + x) *(-4 + 8*x) *|---------- + --------------------|
                         \    3                 3          /
------------------------------------------------------------
                           2                                
                    (1 + x) *(-4 + 8*x)                     
$$\frac{\sqrt[3]{\left(x + 1\right)^{2} \left(8 x - 4\right)} \left(\frac{8 \left(x + 1\right)^{2}}{3} + \frac{\left(2 x + 2\right) \left(8 x - 4\right)}{3}\right)}{\left(x + 1\right)^{2} \left(8 x - 4\right)}$$
((1 + x)^2*(-4 + 8*x))^(1/3)*(8*(1 + x)^2/3 + (-4 + 8*x)*(2 + 2*x)/3)/((1 + x)^2*(-4 + 8*x))
Combinatoria [src]
            _____________________
     2/3 3 /        2            
2*x*2   *\/  (1 + x) *(-1 + 2*x) 
---------------------------------
        (1 + x)*(-1 + 2*x)       
$$\frac{2 \cdot 2^{\frac{2}{3}} x \sqrt[3]{\left(x + 1\right)^{2} \left(2 x - 1\right)}}{\left(x + 1\right) \left(2 x - 1\right)}$$
2*x*2^(2/3)*((1 + x)^2*(-1 + 2*x))^(1/3)/((1 + x)*(-1 + 2*x))
Denominador común [src]
            __________________
     2/3 3 /         3      2 
2*x*2   *\/  -1 + 2*x  + 3*x  
------------------------------
                    2         
        -1 + x + 2*x          
$$\frac{2 \cdot 2^{\frac{2}{3}} x \sqrt[3]{2 x^{3} + 3 x^{2} - 1}}{2 x^{2} + x - 1}$$
2*x*2^(2/3)*(-1 + 2*x^3 + 3*x^2)^(1/3)/(-1 + x + 2*x^2)