Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt((2+x)/(1+x))*(1-(2+x)/(1+x))*(-2/(1+x)-2/(2+x)+(1-(2+x)/(1+x))/(2+x))/(4*(2+x))
¿Cómo vas a descomponer esta sqrt((2+x)/(1+x))*(1-(2+x)/(1+x))*(-2/(1+x)-2/(2+x)+(1-(2+x)/(1+x))/(2+x))/(4*(2+x)) expresión en fracciones?
Solución
Ha introducido
[src]
/ 2 + x\
_______ | 1 - -----|
/ 2 + x / 2 + x\ | 2 2 1 + x|
/ ----- *|1 - -----|*|- ----- - ----- + ---------|
\/ 1 + x \ 1 + x/ \ 1 + x 2 + x 2 + x /
-----------------------------------------------------
4*(2 + x)
$$\frac{\sqrt{\frac{x + 2}{x + 1}} \left(1 - \frac{x + 2}{x + 1}\right) \left(\frac{1 - \frac{x + 2}{x + 1}}{x + 2} + \left(- \frac{2}{x + 2} - \frac{2}{x + 1}\right)\right)}{4 \left(x + 2\right)}$$
((sqrt((2 + x)/(1 + x))*(1 - (2 + x)/(1 + x)))*(-2/(1 + x) - 2/(2 + x) + (1 - (2 + x)/(1 + x))/(2 + x)))/((4*(2 + x)))
Simplificación general
[src]
_______
/ 2 + x
/ ----- *(7/4 + x)
\/ 1 + x
---------------------
2 2
(1 + x) *(2 + x)
$$\frac{\sqrt{\frac{x + 2}{x + 1}} \left(x + \frac{7}{4}\right)}{\left(x + 1\right)^{2} \left(x + 2\right)^{2}}$$
sqrt((2 + x)/(1 + x))*(7/4 + x)/((1 + x)^2*(2 + x)^2)
Compilar la expresión
[src]
/ 2 + x\
_______ | 1 - -----|
/ 2 + x / 2 + x\ | 2 2 1 + x|
/ ----- *|1 - -----|*|- ----- - ----- + ---------|
\/ 1 + x \ 1 + x/ \ 1 + x 2 + x 2 + x /
-----------------------------------------------------
8 + 4*x
$$\frac{\sqrt{\frac{x + 2}{x + 1}} \left(1 - \frac{x + 2}{x + 1}\right) \left(\frac{1 - \frac{x + 2}{x + 1}}{x + 2} - \frac{2}{x + 2} - \frac{2}{x + 1}\right)}{4 x + 8}$$
sqrt((2 + x)/(1 + x))*(1 - (2 + x)/(1 + x))*(-2/(1 + x) - 2/(2 + x) + (1 - (2 + x)/(1 + x))/(2 + x))/(8 + 4*x)
Respuesta numérica
[src]
((2.0 + x)/(1.0 + x))^0.5*(1.0 - (2.0 + x)/(1.0 + x))*(-2.0/(1.0 + x) - 2.0/(2.0 + x) + (1.0 - (2.0 + x)/(1.0 + x))/(2.0 + x))/(8.0 + 4.0*x)
((2.0 + x)/(1.0 + x))^0.5*(1.0 - (2.0 + x)/(1.0 + x))*(-2.0/(1.0 + x) - 2.0/(2.0 + x) + (1.0 - (2.0 + x)/(1.0 + x))/(2.0 + x))/(8.0 + 4.0*x)
Denominador común
[src]
_______________ _______________
/ 2 x / 2 x
7* / ----- + ----- + 4*x* / ----- + -----
\/ 1 + x 1 + x \/ 1 + x 1 + x
-----------------------------------------------
4 3 2
16 + 4*x + 24*x + 48*x + 52*x
$$\frac{4 x \sqrt{\frac{x}{x + 1} + \frac{2}{x + 1}} + 7 \sqrt{\frac{x}{x + 1} + \frac{2}{x + 1}}}{4 x^{4} + 24 x^{3} + 52 x^{2} + 48 x + 16}$$
(7*sqrt(2/(1 + x) + x/(1 + x)) + 4*x*sqrt(2/(1 + x) + x/(1 + x)))/(16 + 4*x^4 + 24*x^3 + 48*x + 52*x^2)
Parte trigonométrica
[src]
/ 2 + x\
_______ | 1 - -----|
/ 2 + x / 2 + x\ | 2 2 1 + x|
/ ----- *|1 - -----|*|- ----- - ----- + ---------|
\/ 1 + x \ 1 + x/ \ 1 + x 2 + x 2 + x /
-----------------------------------------------------
8 + 4*x
$$\frac{\sqrt{\frac{x + 2}{x + 1}} \left(1 - \frac{x + 2}{x + 1}\right) \left(\frac{1 - \frac{x + 2}{x + 1}}{x + 2} - \frac{2}{x + 2} - \frac{2}{x + 1}\right)}{4 x + 8}$$
sqrt((2 + x)/(1 + x))*(1 - (2 + x)/(1 + x))*(-2/(1 + x) - 2/(2 + x) + (1 - (2 + x)/(1 + x))/(2 + x))/(8 + 4*x)
Denominador racional
[src]
_______________ _______________
/ 2 x / 2 x
7* / ----- + ----- + 4*x* / ----- + -----
\/ 1 + x 1 + x \/ 1 + x 1 + x
-----------------------------------------------
2
(1 + x) *(2 + x)*(8 + 4*x)
$$\frac{4 x \sqrt{\frac{x}{x + 1} + \frac{2}{x + 1}} + 7 \sqrt{\frac{x}{x + 1} + \frac{2}{x + 1}}}{\left(x + 1\right)^{2} \left(x + 2\right) \left(4 x + 8\right)}$$
(7*sqrt(2/(1 + x) + x/(1 + x)) + 4*x*sqrt(2/(1 + x) + x/(1 + x)))/((1 + x)^2*(2 + x)*(8 + 4*x))
Combinatoria
[src]
_______
/ 2 + x
/ ----- *(7 + 4*x)
\/ 1 + x
---------------------
2 2
4*(1 + x) *(2 + x)
$$\frac{\sqrt{\frac{x + 2}{x + 1}} \left(4 x + 7\right)}{4 \left(x + 1\right)^{2} \left(x + 2\right)^{2}}$$
sqrt((2 + x)/(1 + x))*(7 + 4*x)/(4*(1 + x)^2*(2 + x)^2)
Unión de expresiones racionales
[src]
_______
/ 2 + x
- / ----- *(-7 - 4*x)
\/ 1 + x
--------------------------
2
(1 + x) *(2 + x)*(8 + 4*x)
$$- \frac{\sqrt{\frac{x + 2}{x + 1}} \left(- 4 x - 7\right)}{\left(x + 1\right)^{2} \left(x + 2\right) \left(4 x + 8\right)}$$
-sqrt((2 + x)/(1 + x))*(-7 - 4*x)/((1 + x)^2*(2 + x)*(8 + 4*x))
Potencias
[src]
/ -2 - x\
_______ | 1 + ------|
/ 2 + x / -2 - x\ | 2 2 1 + x |
/ ----- *|1 + ------|*|- ----- - ----- + ----------|
\/ 1 + x \ 1 + x / \ 1 + x 2 + x 2 + x /
-------------------------------------------------------
8 + 4*x
$$\frac{\sqrt{\frac{x + 2}{x + 1}} \left(\frac{- x - 2}{x + 1} + 1\right) \left(\frac{\frac{- x - 2}{x + 1} + 1}{x + 2} - \frac{2}{x + 2} - \frac{2}{x + 1}\right)}{4 x + 8}$$
/ 2 + x\
_______ | 1 - -----|
/ 2 + x / 2 + x\ | 2 2 1 + x|
/ ----- *|1 - -----|*|- ----- - ----- + ---------|
\/ 1 + x \ 1 + x/ \ 1 + x 2 + x 2 + x /
-----------------------------------------------------
8 + 4*x
$$\frac{\sqrt{\frac{x + 2}{x + 1}} \left(1 - \frac{x + 2}{x + 1}\right) \left(\frac{1 - \frac{x + 2}{x + 1}}{x + 2} - \frac{2}{x + 2} - \frac{2}{x + 1}\right)}{4 x + 8}$$
sqrt((2 + x)/(1 + x))*(1 - (2 + x)/(1 + x))*(-2/(1 + x) - 2/(2 + x) + (1 - (2 + x)/(1 + x))/(2 + x))/(8 + 4*x)