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Simplificación de expresiones/
Descomposición en fracciones simples/
(5(x-1)^2-2(5x-2)(x-1))/(x-1)^4
¿Cómo vas a descomponer esta (5(x-1)^2-2(5x-2)(x-1))/(x-1)^4 expresión en fracciones?
Solución
Ha introducido
[src]
2
5*(x - 1) - 2*(5*x - 2)*(x - 1)
--------------------------------
4
(x - 1)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) 2 \left(5 x - 2\right)}{\left(x - 1\right)^{4}}$$
(5*(x - 1)^2 - 2*(5*x - 2)*(x - 1))/(x - 1)^4
Descomposición de una fracción
[src]
-6/(-1 + x)^3 - 5/(-1 + x)^2
$$- \frac{5}{\left(x - 1\right)^{2}} - \frac{6}{\left(x - 1\right)^{3}}$$
6 5
- --------- - ---------
3 2
(-1 + x) (-1 + x)
Simplificación general
[src]
-(1 + 5*x)
-----------
3
(-1 + x)
$$- \frac{5 x + 1}{\left(x - 1\right)^{3}}$$
-(1 + 5*x)/(-1 + x)^3
Respuesta numérica
[src]
(5.0*(-1.0 + x)^2 - (-1.0 + x)*(-4.0 + 10.0*x))/(-1.0 + x)^4
(5.0*(-1.0 + x)^2 - (-1.0 + x)*(-4.0 + 10.0*x))/(-1.0 + x)^4
Parte trigonométrica
[src]
2
5*(-1 + x) - (-1 + x)*(-4 + 10*x)
----------------------------------
4
(-1 + x)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) \left(10 x - 4\right)}{\left(x - 1\right)^{4}}$$
(5*(-1 + x)^2 - (-1 + x)*(-4 + 10*x))/(-1 + x)^4
Compilar la expresión
[src]
2
5*(-1 + x) - (-1 + x)*(-4 + 10*x)
----------------------------------
4
(-1 + x)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) \left(10 x - 4\right)}{\left(x - 1\right)^{4}}$$
(5*(-1 + x)^2 - (-1 + x)*(-4 + 10*x))/(-1 + x)^4
Unión de expresiones racionales
[src]
-1 - 5*x
---------
3
(-1 + x)
$$\frac{- 5 x - 1}{\left(x - 1\right)^{3}}$$
(-1 - 5*x)/(-1 + x)^3
Denominador racional
[src]
2
5*(-1 + x) - (-1 + x)*(-4 + 10*x)
----------------------------------
4
(-1 + x)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) \left(10 x - 4\right)}{\left(x - 1\right)^{4}}$$
(5*(-1 + x)^2 - (-1 + x)*(-4 + 10*x))/(-1 + x)^4
Denominador común
[src]
-(1 + 5*x)
--------------------
3 2
-1 + x - 3*x + 3*x
$$- \frac{5 x + 1}{x^{3} - 3 x^{2} + 3 x - 1}$$
-(1 + 5*x)/(-1 + x^3 - 3*x^2 + 3*x)
Combinatoria
[src]
-(1 + 5*x)
-----------
3
(-1 + x)
$$- \frac{5 x + 1}{\left(x - 1\right)^{3}}$$
-(1 + 5*x)/(-1 + x)^3
Potencias
[src]
2
5*(-1 + x) - (-1 + x)*(-4 + 10*x)
----------------------------------
4
(-1 + x)
$$\frac{5 \left(x - 1\right)^{2} - \left(x - 1\right) \left(10 x - 4\right)}{\left(x - 1\right)^{4}}$$
(5*(-1 + x)^2 - (-1 + x)*(-4 + 10*x))/(-1 + x)^4