Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
((x+1)^2/(x-1)^2)*(x-1)*(2/(x-1)-2*(x+1)/(x-1)^2)/(x+1)
¿Cómo vas a descomponer esta ((x+1)^2/(x-1)^2)*(x-1)*(2/(x-1)-2*(x+1)/(x-1)^2)/(x+1) expresión en fracciones?
Solución
Ha introducido
[src]
2
(x + 1) / 2 2*(x + 1)\
--------*(x - 1)*|----- - ---------|
2 |x - 1 2|
(x - 1) \ (x - 1) /
------------------------------------
x + 1
$$\frac{\frac{\left(x + 1\right)^{2}}{\left(x - 1\right)^{2}} \left(x - 1\right) \left(- \frac{2 \left(x + 1\right)}{\left(x - 1\right)^{2}} + \frac{2}{x - 1}\right)}{x + 1}$$
((((x + 1)^2/(x - 1)^2)*(x - 1))*(2/(x - 1) - 2*(x + 1)/(x - 1)^2))/(x + 1)
Descomposición de una fracción
[src]
-8/(-1 + x)^3 - 4/(-1 + x)^2
$$- \frac{4}{\left(x - 1\right)^{2}} - \frac{8}{\left(x - 1\right)^{3}}$$
8 4
- --------- - ---------
3 2
(-1 + x) (-1 + x)
Simplificación general
[src]
-(4 + 4*x)
-----------
3
(-1 + x)
$$- \frac{4 x + 4}{\left(x - 1\right)^{3}}$$
-(4 + 4*x)/(-1 + x)^3
Compilar la expresión
[src]
/ 2 2 + 2*x \
(1 + x)*|------ - ---------|
|-1 + x 2|
\ (-1 + x) /
----------------------------
-1 + x
$$\frac{\left(x + 1\right) \left(\frac{2}{x - 1} - \frac{2 x + 2}{\left(x - 1\right)^{2}}\right)}{x - 1}$$
(1 + x)*(2/(-1 + x) - (2 + 2*x)/(-1 + x)^2)/(-1 + x)
Parte trigonométrica
[src]
/ 2 2 + 2*x \
(1 + x)*|------ - ---------|
|-1 + x 2|
\ (-1 + x) /
----------------------------
-1 + x
$$\frac{\left(x + 1\right) \left(\frac{2}{x - 1} - \frac{2 x + 2}{\left(x - 1\right)^{2}}\right)}{x - 1}$$
(1 + x)*(2/(-1 + x) - (2 + 2*x)/(-1 + x)^2)/(-1 + x)
Unión de expresiones racionales
[src]
-4*(1 + x)
----------
3
(-1 + x)
$$- \frac{4 \left(x + 1\right)}{\left(x - 1\right)^{3}}$$
-4*(1 + x)/(-1 + x)^3
Combinatoria
[src]
-4*(1 + x)
----------
3
(-1 + x)
$$- \frac{4 \left(x + 1\right)}{\left(x - 1\right)^{3}}$$
-4*(1 + x)/(-1 + x)^3
Potencias
[src]
/ 2 -2 - 2*x\
(1 + x)*|------ + ---------|
|-1 + x 2|
\ (-1 + x) /
----------------------------
-1 + x
$$\frac{\left(x + 1\right) \left(\frac{- 2 x - 2}{\left(x - 1\right)^{2}} + \frac{2}{x - 1}\right)}{x - 1}$$
/ 2 2 + 2*x \
(1 + x)*|------ - ---------|
|-1 + x 2|
\ (-1 + x) /
----------------------------
-1 + x
$$\frac{\left(x + 1\right) \left(\frac{2}{x - 1} - \frac{2 x + 2}{\left(x - 1\right)^{2}}\right)}{x - 1}$$
(1 + x)*(2/(-1 + x) - (2 + 2*x)/(-1 + x)^2)/(-1 + x)
Denominador común
[src]
-(4 + 4*x)
--------------------
3 2
-1 + x - 3*x + 3*x
$$- \frac{4 x + 4}{x^{3} - 3 x^{2} + 3 x - 1}$$
-(4 + 4*x)/(-1 + x^3 - 3*x^2 + 3*x)
Denominador racional
[src]
/ 2 \
(1 + x)*\2*(-1 + x) + (-1 + x)*(-2 - 2*x)/
-------------------------------------------
4
(-1 + x)
$$\frac{\left(x + 1\right) \left(\left(- 2 x - 2\right) \left(x - 1\right) + 2 \left(x - 1\right)^{2}\right)}{\left(x - 1\right)^{4}}$$
(1 + x)*(2*(-1 + x)^2 + (-1 + x)*(-2 - 2*x))/(-1 + x)^4
Respuesta numérica
[src]
(1.0 + x)*(2.0/(-1.0 + x) - (2.0 + 2.0*x)/(-1.0 + x)^2)/(-1.0 + x)
(1.0 + x)*(2.0/(-1.0 + x) - (2.0 + 2.0*x)/(-1.0 + x)^2)/(-1.0 + x)