Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt((x/(x+1))^2)*(x+1)*(2/(x+1)-2*x/(x+1)^2)/(2*x)
¿Cómo vas a descomponer esta sqrt((x/(x+1))^2)*(x+1)*(2/(x+1)-2*x/(x+1)^2)/(2*x) expresión en fracciones?
Solución
Ha introducido
[src]
__________
/ 2
/ / x \ / 2 2*x \
/ |-----| *(x + 1)*|----- - --------|
\/ \x + 1/ |x + 1 2|
\ (x + 1) /
------------------------------------------
2*x
$$\frac{\left(x + 1\right) \sqrt{\left(\frac{x}{x + 1}\right)^{2}} \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right)}{2 x}$$
((sqrt((x/(x + 1))^2)*(x + 1))*(2/(x + 1) - 2*x/(x + 1)^2))/((2*x))
Simplificación general
[src]
__________
/ 2
/ x
/ --------
/ 2
\/ (1 + x)
----------------
x*(1 + x)
$$\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}}}{x \left(x + 1\right)}$$
sqrt(x^2/(1 + x)^2)/(x*(1 + x))
Respuesta numérica
[src]
0.5*(x^2/(1.0 + x)^2)^0.5*(1.0 + x)*(2.0/(1.0 + x) - 2.0*x/(1.0 + x)^2)/x
0.5*(x^2/(1.0 + x)^2)^0.5*(1.0 + x)*(2.0/(1.0 + x) - 2.0*x/(1.0 + x)^2)/x
Denominador racional
[src]
__________ __________ __________
/ 2 / 2 / 2
/ x 2 / x / x 2
- 2*x* / -------- - 2*x * / -------- + 2* / -------- *(1 + x)
/ 2 / 2 / 2
\/ (x + 1) \/ (x + 1) \/ (x + 1)
----------------------------------------------------------------------------
2
2*x*(1 + x)
$$\frac{- 2 x^{2} \sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} - 2 x \sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} + 2 \sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} \left(x + 1\right)^{2}}{2 x \left(x + 1\right)^{2}}$$
(-2*x*sqrt(x^2/(x + 1)^2) - 2*x^2*sqrt(x^2/(x + 1)^2) + 2*sqrt(x^2/(x + 1)^2)*(1 + x)^2)/(2*x*(1 + x)^2)
Unión de expresiones racionales
[src]
__________
/ 2
/ x
/ --------
/ 2
\/ (1 + x)
----------------
x*(1 + x)
$$\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}}}{x \left(x + 1\right)}$$
sqrt(x^2/(1 + x)^2)/(x*(1 + x))
Parte trigonométrica
[src]
__________
/ 2
/ x / 2 2*x \
/ -------- *(1 + x)*|----- - --------|
/ 2 |1 + x 2|
\/ (1 + x) \ (1 + x) /
-------------------------------------------
2*x
$$\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} \left(x + 1\right) \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right)}{2 x}$$
sqrt(x^2/(1 + x)^2)*(1 + x)*(2/(1 + x) - 2*x/(1 + x)^2)/(2*x)
Potencias
[src]
__________
/ 2
/ x / 2 2*x \
/ -------- *(1 + x)*|----- - --------|
/ 2 |1 + x 2|
\/ (1 + x) \ (1 + x) /
-------------------------------------------
2*x
$$\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} \left(x + 1\right) \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right)}{2 x}$$
sqrt(x^2/(1 + x)^2)*(1 + x)*(2/(1 + x) - 2*x/(1 + x)^2)/(2*x)
Combinatoria
[src]
______________
/ 2
/ x
/ ------------
/ 2
\/ 1 + x + 2*x
--------------------
x*(1 + x)
$$\frac{\sqrt{\frac{x^{2}}{x^{2} + 2 x + 1}}}{x \left(x + 1\right)}$$
sqrt(x^2/(1 + x^2 + 2*x))/(x*(1 + x))
Compilar la expresión
[src]
__________
/ 2
/ x / 2 2*x \
/ -------- *(1 + x)*|----- - --------|
/ 2 |1 + x 2|
\/ (1 + x) \ (1 + x) /
-------------------------------------------
2*x
$$\frac{\sqrt{\frac{x^{2}}{\left(x + 1\right)^{2}}} \left(x + 1\right) \left(- \frac{2 x}{\left(x + 1\right)^{2}} + \frac{2}{x + 1}\right)}{2 x}$$
sqrt(x^2/(1 + x)^2)*(1 + x)*(2/(1 + x) - 2*x/(1 + x)^2)/(2*x)
Denominador común
[src]
______________
/ 2
/ x
/ ------------
/ 2
\/ 1 + x + 2*x
--------------------
2
x + x
$$\frac{\sqrt{\frac{x^{2}}{x^{2} + 2 x + 1}}}{x^{2} + x}$$
sqrt(x^2/(1 + x^2 + 2*x))/(x + x^2)