Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
-((-1+x^2/(1+x^2))/sqrt(1+x^2)+(1+x/sqrt(1+x^2))^2/(x+sqrt(1+x^2)))/(x+sqrt(1+x^2))
¿Cómo vas a descomponer esta -((-1+x^2/(1+x^2))/sqrt(1+x^2)+(1+x/sqrt(1+x^2))^2/(x+sqrt(1+x^2)))/(x+sqrt(1+x^2)) expresión en fracciones?
Solución
Ha introducido
[src]
2
2 / x \
x |1 + -----------|
-1 + ------ | ________|
2 | / 2 |
1 + x \ \/ 1 + x /
- ----------- - ------------------
________ ________
/ 2 / 2
\/ 1 + x x + \/ 1 + x
----------------------------------
________
/ 2
x + \/ 1 + x
$$\frac{- \frac{\frac{x^{2}}{x^{2} + 1} - 1}{\sqrt{x^{2} + 1}} - \frac{\left(\frac{x}{\sqrt{x^{2} + 1}} + 1\right)^{2}}{x + \sqrt{x^{2} + 1}}}{x + \sqrt{x^{2} + 1}}$$
(-(-1 + x^2/(1 + x^2))/sqrt(1 + x^2) - (1 + x/sqrt(1 + x^2))^2/(x + sqrt(1 + x^2)))/(x + sqrt(1 + x^2))
Simplificación general
[src]
3/2 / ________\
2 / 2\ | / 2 |
1 + x - \1 + x / *\x + \/ 1 + x /
--------------------------------------
5/2 / ________\
/ 2\ | / 2 |
\1 + x / *\x + \/ 1 + x /
$$\frac{x^{2} - \left(x + \sqrt{x^{2} + 1}\right) \left(x^{2} + 1\right)^{\frac{3}{2}} + 1}{\left(x + \sqrt{x^{2} + 1}\right) \left(x^{2} + 1\right)^{\frac{5}{2}}}$$
(1 + x^2 - (1 + x^2)^(3/2)*(x + sqrt(1 + x^2)))/((1 + x^2)^(5/2)*(x + sqrt(1 + x^2)))
Denominador común
[src]
/ ________\
| 3 2 / 2 |
-\x + 2*x + 2*x *\/ 1 + x /
---------------------------------------------------------------------
________ ________ ________
/ 2 5 3 4 / 2 2 / 2
\/ 1 + x + 2*x + 2*x + 4*x + 2*x *\/ 1 + x + 3*x *\/ 1 + x
$$- \frac{2 x^{3} + 2 x^{2} \sqrt{x^{2} + 1} + x}{2 x^{5} + 2 x^{4} \sqrt{x^{2} + 1} + 4 x^{3} + 3 x^{2} \sqrt{x^{2} + 1} + 2 x + \sqrt{x^{2} + 1}}$$
-(x + 2*x^3 + 2*x^2*sqrt(1 + x^2))/(sqrt(1 + x^2) + 2*x + 2*x^5 + 4*x^3 + 2*x^4*sqrt(1 + x^2) + 3*x^2*sqrt(1 + x^2))
Potencias
[src]
2
2 / x \
x |1 + -----------|
1 - ------ | ________|
2 | / 2 |
1 + x \ \/ 1 + x /
----------- - ------------------
________ ________
/ 2 / 2
\/ 1 + x x + \/ 1 + x
--------------------------------
________
/ 2
x + \/ 1 + x
$$\frac{\frac{- \frac{x^{2}}{x^{2} + 1} + 1}{\sqrt{x^{2} + 1}} - \frac{\left(\frac{x}{\sqrt{x^{2} + 1}} + 1\right)^{2}}{x + \sqrt{x^{2} + 1}}}{x + \sqrt{x^{2} + 1}}$$
((1 - x^2/(1 + x^2))/sqrt(1 + x^2) - (1 + x/sqrt(1 + x^2))^2/(x + sqrt(1 + x^2)))/(x + sqrt(1 + x^2))
Denominador racional
[src]
2 / 2\
/ ________\ | ________ ________ 2 / ________\ |
| / 2 | | 4 2 / 2 3 / 2 / 2\ | / 2 | |
\x - \/ 1 + x / *\1 + x + 2*x + x*\/ 1 + x + x *\/ 1 + x - \1 + x / *\x + \/ 1 + x / /
--------------------------------------------------------------------------------------------------
6 2 4
1 + x + 3*x + 3*x
$$\frac{\left(x - \sqrt{x^{2} + 1}\right)^{2} \left(x^{4} + x^{3} \sqrt{x^{2} + 1} + 2 x^{2} + x \sqrt{x^{2} + 1} - \left(x + \sqrt{x^{2} + 1}\right)^{2} \left(x^{2} + 1\right)^{2} + 1\right)}{x^{6} + 3 x^{4} + 3 x^{2} + 1}$$
(x - sqrt(1 + x^2))^2*(1 + x^4 + 2*x^2 + x*sqrt(1 + x^2) + x^3*sqrt(1 + x^2) - (1 + x^2)^2*(x + sqrt(1 + x^2))^2)/(1 + x^6 + 3*x^2 + 3*x^4)
Respuesta numérica
[src]
(-(1.0 + x^2)^(-0.5)*(-1.0 + x^2/(1.0 + x^2)) - (1.0 + x*(1.0 + x^2)^(-0.5))^2/(x + (1.0 + x^2)^0.5))/(x + (1.0 + x^2)^0.5)
(-(1.0 + x^2)^(-0.5)*(-1.0 + x^2/(1.0 + x^2)) - (1.0 + x*(1.0 + x^2)^(-0.5))^2/(x + (1.0 + x^2)^0.5))/(x + (1.0 + x^2)^0.5)
Unión de expresiones racionales
[src]
3/2 / ________\
2 / 2\ | / 2 |
1 + x - \1 + x / *\x + \/ 1 + x /
--------------------------------------
5/2 / ________\
/ 2\ | / 2 |
\1 + x / *\x + \/ 1 + x /
$$\frac{x^{2} - \left(x + \sqrt{x^{2} + 1}\right) \left(x^{2} + 1\right)^{\frac{3}{2}} + 1}{\left(x + \sqrt{x^{2} + 1}\right) \left(x^{2} + 1\right)^{\frac{5}{2}}}$$
(1 + x^2 - (1 + x^2)^(3/2)*(x + sqrt(1 + x^2)))/((1 + x^2)^(5/2)*(x + sqrt(1 + x^2)))
Combinatoria
[src]
-x
-----------
3/2
/ 2\
\1 + x /
$$- \frac{x}{\left(x^{2} + 1\right)^{\frac{3}{2}}}$$
-x/(1 + x^2)^(3/2)