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Simplificación de expresiones/ Descomposición en fracciones simples/ acos(2*x)^4/(3*(x-3)^(2/3))-8*(x-3)^(1/3)*acos(2*x)^3/sqrt(1-4*x^2)

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

Expresión a simplificar:

Solución

Ha introducido [src] 
     4           3 _______     3     
 acos (2*x)    8*\/ x - 3 *acos (2*x)
------------ - ----------------------
         2/3          __________     
3*(x - 3)            /        2      
                   \/  1 - 4*x
$$- \frac{8 \sqrt[3]{x - 3} \operatorname{acos}^{3}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}} + \frac{\operatorname{acos}^{4}{\left(2 x \right)}}{3 \left(x - 3\right)^{\frac{2}{3}}}$$ 
acos(2*x)^4/((3*(x - 3)^(2/3))) - (8*(x - 3)^(1/3))*acos(2*x)^3/sqrt(1 - 4*x^2)
Simplificación general [src] 
           /               __________          \
    3      |              /        2           |
acos (2*x)*\72 - 24*x + \/  1 - 4*x  *acos(2*x)/
------------------------------------------------
               __________                       
              /        2          2/3           
          3*\/  1 - 4*x  *(-3 + x)
$$\frac{\left(- 24 x + \sqrt{1 - 4 x^{2}} \operatorname{acos}{\left(2 x \right)} + 72\right) \operatorname{acos}^{3}{\left(2 x \right)}}{3 \sqrt{1 - 4 x^{2}} \left(x - 3\right)^{\frac{2}{3}}}$$ 
acos(2*x)^3*(72 - 24*x + sqrt(1 - 4*x^2)*acos(2*x))/(3*sqrt(1 - 4*x^2)*(-3 + x)^(2/3))
Respuesta numérica [src] 
0.160249952256379*(-1 + 0.333333333333333*x)^(-0.666666666666667)*acos(2*x)^4 - 5.76899828122963*(-1 + 0.333333333333333*x)^0.333333333333333*(0.25 - x^2)^(-0.5)*acos(2*x)^3
0.160249952256379*(-1 + 0.333333333333333*x)^(-0.666666666666667)*acos(2*x)^4 - 5.76899828122963*(-1 + 0.333333333333333*x)^0.333333333333333*(0.25 - x^2)^(-0.5)*acos(2*x)^3
Parte trigonométrica [src] 
      4           3 ________     3     
  acos (2*x)    8*\/ -3 + x *acos (2*x)
------------- - -----------------------
          2/3           __________     
3*(-3 + x)             /        2      
                     \/  1 - 4*x
$$\frac{\operatorname{acos}^{4}{\left(2 x \right)}}{3 \left(x - 3\right)^{\frac{2}{3}}} - \frac{8 \sqrt[3]{x - 3} \operatorname{acos}^{3}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}$$ 
acos(2*x)^4/(3*(-3 + x)^(2/3)) - 8*(-3 + x)^(1/3)*acos(2*x)^3/sqrt(1 - 4*x^2)
Unión de expresiones racionales [src] 
           /               __________          \
    3      |              /        2           |
acos (2*x)*\72 - 24*x + \/  1 - 4*x  *acos(2*x)/
------------------------------------------------
               __________                       
              /        2          2/3           
          3*\/  1 - 4*x  *(-3 + x)
$$\frac{\left(- 24 x + \sqrt{1 - 4 x^{2}} \operatorname{acos}{\left(2 x \right)} + 72\right) \operatorname{acos}^{3}{\left(2 x \right)}}{3 \sqrt{1 - 4 x^{2}} \left(x - 3\right)^{\frac{2}{3}}}$$ 
acos(2*x)^3*(72 - 24*x + sqrt(1 - 4*x^2)*acos(2*x))/(3*sqrt(1 - 4*x^2)*(-3 + x)^(2/3))
Combinatoria [src] 
            /                __________          \ 
     3      |               /        2           | 
-acos (2*x)*\-72 + 24*x - \/  1 - 4*x  *acos(2*x)/ 
---------------------------------------------------
          _______________________         2/3      
      3*\/ -(1 + 2*x)*(-1 + 2*x) *(-3 + x)
$$- \frac{\left(24 x - \sqrt{1 - 4 x^{2}} \operatorname{acos}{\left(2 x \right)} - 72\right) \operatorname{acos}^{3}{\left(2 x \right)}}{3 \sqrt{- \left(2 x - 1\right) \left(2 x + 1\right)} \left(x - 3\right)^{\frac{2}{3}}}$$ 
-acos(2*x)^3*(-72 + 24*x - sqrt(1 - 4*x^2)*acos(2*x))/(3*sqrt(-(1 + 2*x)*(-1 + 2*x))*(-3 + x)^(2/3))
Potencias [src] 
      4           3 ________     3     
  acos (2*x)    8*\/ -3 + x *acos (2*x)
------------- - -----------------------
          2/3           __________     
3*(-3 + x)             /        2      
                     \/  1 - 4*x
$$\frac{\operatorname{acos}^{4}{\left(2 x \right)}}{3 \left(x - 3\right)^{\frac{2}{3}}} - \frac{8 \sqrt[3]{x - 3} \operatorname{acos}^{3}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}$$ 
acos(2*x)^4/(3*(-3 + x)^(2/3)) - 8*(-3 + x)^(1/3)*acos(2*x)^3/sqrt(1 - 4*x^2)
Denominador racional [src] 
                     __________                                        __________           
      4             /        2      3           2     4               /        2      3     
- acos (2*x) - 72*\/  1 - 4*x  *acos (2*x) + 4*x *acos (2*x) + 24*x*\/  1 - 4*x  *acos (2*x)
--------------------------------------------------------------------------------------------
                                   /        2\         2/3                                  
                                 3*\-1 + 4*x /*(-3 + x)
$$\frac{4 x^{2} \operatorname{acos}^{4}{\left(2 x \right)} + 24 x \sqrt{1 - 4 x^{2}} \operatorname{acos}^{3}{\left(2 x \right)} - 72 \sqrt{1 - 4 x^{2}} \operatorname{acos}^{3}{\left(2 x \right)} - \operatorname{acos}^{4}{\left(2 x \right)}}{3 \left(x - 3\right)^{\frac{2}{3}} \left(4 x^{2} - 1\right)}$$ 
(-acos(2*x)^4 - 72*sqrt(1 - 4*x^2)*acos(2*x)^3 + 4*x^2*acos(2*x)^4 + 24*x*sqrt(1 - 4*x^2)*acos(2*x)^3)/(3*(-1 + 4*x^2)*(-3 + x)^(2/3))
Compilar la expresión [src] 
      4           3 ________     3     
  acos (2*x)    8*\/ -3 + x *acos (2*x)
------------- - -----------------------
          2/3           __________     
3*(-3 + x)             /        2      
                     \/  1 - 4*x
$$\frac{\operatorname{acos}^{4}{\left(2 x \right)}}{3 \left(x - 3\right)^{\frac{2}{3}}} - \frac{8 \sqrt[3]{x - 3} \operatorname{acos}^{3}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}$$ 
acos(2*x)^4/(3*(-3 + x)^(2/3)) - 8*(-3 + x)^(1/3)*acos(2*x)^3/sqrt(1 - 4*x^2)
Denominador común [src] 
 /                     __________                             \ 
 |         3          /        2      4                 3     | 
-\- 72*acos (2*x) - \/  1 - 4*x  *acos (2*x) + 24*x*acos (2*x)/ 
----------------------------------------------------------------
                       __________                               
                      /        2          2/3                   
                  3*\/  1 - 4*x  *(-3 + x)
$$- \frac{24 x \operatorname{acos}^{3}{\left(2 x \right)} - \sqrt{1 - 4 x^{2}} \operatorname{acos}^{4}{\left(2 x \right)} - 72 \operatorname{acos}^{3}{\left(2 x \right)}}{3 \sqrt{1 - 4 x^{2}} \left(x - 3\right)^{\frac{2}{3}}}$$ 
-(-72*acos(2*x)^3 - sqrt(1 - 4*x^2)*acos(2*x)^4 + 24*x*acos(2*x)^3)/(3*sqrt(1 - 4*x^2)*(-3 + x)^(2/3))
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