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Simplificación de expresiones/
Descomposición en fracciones simples/
6*(-1-(8+x^2)/(1+x)^2+2*x/(1+x))/(1+x)^2
¿Cómo vas a descomponer esta 6*(-1-(8+x^2)/(1+x)^2+2*x/(1+x))/(1+x)^2 expresión en fracciones?
Solución
Ha introducido
[src]
/ 2 \
| 8 + x 2*x |
6*|-1 - -------- + -----|
| 2 1 + x|
\ (1 + x) /
-------------------------
2
(1 + x)
$$\frac{6 \left(\frac{2 x}{x + 1} + \left(-1 - \frac{x^{2} + 8}{\left(x + 1\right)^{2}}\right)\right)}{\left(x + 1\right)^{2}}$$
(6*(-1 - (8 + x^2)/(1 + x)^2 + (2*x)/(1 + x)))/(1 + x)^2
Descomposición de una fracción
[src]
-54/(1 + x)^4
$$- \frac{54}{\left(x + 1\right)^{4}}$$
-54
--------
4
(1 + x)
Simplificación general
[src]
-54
--------------------------
4 3 2
1 + x + 4*x + 4*x + 6*x
$$- \frac{54}{x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1}$$
-54/(1 + x^4 + 4*x + 4*x^3 + 6*x^2)
Respuesta numérica
[src]
(-6.0 + 12.0*x/(1.0 + x) - 6.0*(8.0 + x^2)/(1.0 + x)^2)/(1.0 + x)^2
(-6.0 + 12.0*x/(1.0 + x) - 6.0*(8.0 + x^2)/(1.0 + x)^2)/(1.0 + x)^2
Compilar la expresión
[src]
/ 2\
6*\8 + x / 12*x
-6 - ---------- + -----
2 1 + x
(1 + x)
-----------------------
2
(1 + x)
$$\frac{\frac{12 x}{x + 1} - 6 - \frac{6 \left(x^{2} + 8\right)}{\left(x + 1\right)^{2}}}{\left(x + 1\right)^{2}}$$
(-6 - 6*(8 + x^2)/(1 + x)^2 + 12*x/(1 + x))/(1 + x)^2
Unión de expresiones racionales
[src]
/ 2 2 \
6*\-8 - x - (1 + x) + 2*x*(1 + x)/
------------------------------------
4
(1 + x)
$$\frac{6 \left(- x^{2} + 2 x \left(x + 1\right) - \left(x + 1\right)^{2} - 8\right)}{\left(x + 1\right)^{4}}$$
6*(-8 - x^2 - (1 + x)^2 + 2*x*(1 + x))/(1 + x)^4
Denominador común
[src]
-54
--------------------------
4 3 2
1 + x + 4*x + 4*x + 6*x
$$- \frac{54}{x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1}$$
-54/(1 + x^4 + 4*x + 4*x^3 + 6*x^2)
Parte trigonométrica
[src]
/ 2\
6*\8 + x / 12*x
-6 - ---------- + -----
2 1 + x
(1 + x)
-----------------------
2
(1 + x)
$$\frac{\frac{12 x}{x + 1} - 6 - \frac{6 \left(x^{2} + 8\right)}{\left(x + 1\right)^{2}}}{\left(x + 1\right)^{2}}$$
(-6 - 6*(8 + x^2)/(1 + x)^2 + 12*x/(1 + x))/(1 + x)^2
Denominador racional
[src]
/ 2 2\ 2
6*(1 + x)*\-8 - x - (1 + x) / + 12*x*(1 + x)
----------------------------------------------
5
(1 + x)
$$\frac{12 x \left(x + 1\right)^{2} + 6 \left(x + 1\right) \left(- x^{2} - \left(x + 1\right)^{2} - 8\right)}{\left(x + 1\right)^{5}}$$
(6*(1 + x)*(-8 - x^2 - (1 + x)^2) + 12*x*(1 + x)^2)/(1 + x)^5
Potencias
[src]
/ 2\
6*\-8 - x / 12*x
-6 + ----------- + -----
2 1 + x
(1 + x)
------------------------
2
(1 + x)
$$\frac{\frac{12 x}{x + 1} - 6 + \frac{6 \left(- x^{2} - 8\right)}{\left(x + 1\right)^{2}}}{\left(x + 1\right)^{2}}$$
/ 2\
6*\8 + x / 12*x
-6 - ---------- + -----
2 1 + x
(1 + x)
-----------------------
2
(1 + x)
$$\frac{\frac{12 x}{x + 1} - 6 - \frac{6 \left(x^{2} + 8\right)}{\left(x + 1\right)^{2}}}{\left(x + 1\right)^{2}}$$
2
-48 - 6*x 12*x
-6 + ---------- + -----
2 1 + x
(1 + x)
-----------------------
2
(1 + x)
$$\frac{\frac{12 x}{x + 1} - 6 + \frac{- 6 x^{2} - 48}{\left(x + 1\right)^{2}}}{\left(x + 1\right)^{2}}$$
(-6 + (-48 - 6*x^2)/(1 + x)^2 + 12*x/(1 + x))/(1 + x)^2