Sr Examen
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?
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))