Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt((x-3)/(x+3))*(x+3)*(1/(2*(x+3))-(x-3)/(2*(x+3)^2))/(x-3)
¿Cómo vas a descomponer esta sqrt((x-3)/(x+3))*(x+3)*(1/(2*(x+3))-(x-3)/(2*(x+3)^2))/(x-3) expresión en fracciones?
Solución
Ha introducido
[src]
_______
/ x - 3 / 1 x - 3 \
/ ----- *(x + 3)*|--------- - ----------|
\/ x + 3 |2*(x + 3) 2|
\ 2*(x + 3) /
--------------------------------------------
x - 3
$$\frac{\sqrt{\frac{x - 3}{x + 3}} \left(x + 3\right) \left(- \frac{x - 3}{2 \left(x + 3\right)^{2}} + \frac{1}{2 \left(x + 3\right)}\right)}{x - 3}$$
((sqrt((x - 3)/(x + 3))*(x + 3))*(1/(2*(x + 3)) - (x - 3)/(2*(x + 3)^2)))/(x - 3)
Simplificación general
[src]
________
/ -3 + x
3* / ------
\/ 3 + x
--------------
2
-9 + x
$$\frac{3 \sqrt{\frac{x - 3}{x + 3}}}{x^{2} - 9}$$
3*sqrt((-3 + x)/(3 + x))/(-9 + x^2)
Respuesta numérica
[src]
((-3.0 + x)/(3.0 + x))^0.5*(3.0 + x)*(1/(6.0 + 2.0*x) - 0.0555555555555556*(-3.0 + x)/(1 + 0.333333333333333*x)^2)/(-3.0 + x)
((-3.0 + x)/(3.0 + x))^0.5*(3.0 + x)*(1/(6.0 + 2.0*x) - 0.0555555555555556*(-3.0 + x)/(1 + 0.333333333333333*x)^2)/(-3.0 + x)
Denominador racional
[src]
_________________ _________________ _________________
/ 3 x 2 / 3 x 2 / 3 x
18* / - ----- + ----- - 2*x * / - ----- + ----- + 2*(3 + x) * / - ----- + -----
\/ x + 3 x + 3 \/ x + 3 x + 3 \/ x + 3 x + 3
----------------------------------------------------------------------------------------
2*(-3 + x)*(3 + x)*(6 + 2*x)
$$\frac{- 2 x^{2} \sqrt{\frac{x}{x + 3} - \frac{3}{x + 3}} + 2 \left(x + 3\right)^{2} \sqrt{\frac{x}{x + 3} - \frac{3}{x + 3}} + 18 \sqrt{\frac{x}{x + 3} - \frac{3}{x + 3}}}{2 \left(x - 3\right) \left(x + 3\right) \left(2 x + 6\right)}$$
(18*sqrt(-3/(x + 3) + x/(x + 3)) - 2*x^2*sqrt(-3/(x + 3) + x/(x + 3)) + 2*(3 + x)^2*sqrt(-3/(x + 3) + x/(x + 3)))/(2*(-3 + x)*(3 + x)*(6 + 2*x))
Unión de expresiones racionales
[src]
________
/ -3 + x
3* / ------
\/ 3 + x
----------------
(-3 + x)*(3 + x)
$$\frac{3 \sqrt{\frac{x - 3}{x + 3}}}{\left(x - 3\right) \left(x + 3\right)}$$
3*sqrt((-3 + x)/(3 + x))/((-3 + x)*(3 + x))
Combinatoria
[src]
________
/ -3 + x
3* / ------
\/ 3 + x
----------------
(-3 + x)*(3 + x)
$$\frac{3 \sqrt{\frac{x - 3}{x + 3}}}{\left(x - 3\right) \left(x + 3\right)}$$
3*sqrt((-3 + x)/(3 + x))/((-3 + x)*(3 + x))
Compilar la expresión
[src]
________
/ -3 + x / 1 -3 + x \
/ ------ *(3 + x)*|------- - ----------|
\/ 3 + x |6 + 2*x 2|
\ 2*(3 + x) /
-------------------------------------------
-3 + x
$$\frac{\sqrt{\frac{x - 3}{x + 3}} \left(x + 3\right) \left(- \frac{x - 3}{2 \left(x + 3\right)^{2}} + \frac{1}{2 x + 6}\right)}{x - 3}$$
sqrt((-3 + x)/(3 + x))*(3 + x)*(1/(6 + 2*x) - (-3 + x)/(2*(3 + x)^2))/(-3 + x)
Parte trigonométrica
[src]
________
/ -3 + x / 1 -3 + x \
/ ------ *(3 + x)*|------- - ----------|
\/ 3 + x |6 + 2*x 2|
\ 2*(3 + x) /
-------------------------------------------
-3 + x
$$\frac{\sqrt{\frac{x - 3}{x + 3}} \left(x + 3\right) \left(- \frac{x - 3}{2 \left(x + 3\right)^{2}} + \frac{1}{2 x + 6}\right)}{x - 3}$$
sqrt((-3 + x)/(3 + x))*(3 + x)*(1/(6 + 2*x) - (-3 + x)/(2*(3 + x)^2))/(-3 + x)
Denominador común
[src]
_________________
/ 3 x
3* / - ----- + -----
\/ 3 + x 3 + x
-----------------------
2
-9 + x
$$\frac{3 \sqrt{\frac{x}{x + 3} - \frac{3}{x + 3}}}{x^{2} - 9}$$
3*sqrt(-3/(3 + x) + x/(3 + x))/(-9 + x^2)
Potencias
[src]
/ 3 x \
________ | - - - |
/ -3 + x | 1 2 2 |
/ ------ *(3 + x)*|------- + --------|
\/ 3 + x |6 + 2*x 2|
\ (3 + x) /
-----------------------------------------
-3 + x
$$\frac{\sqrt{\frac{x - 3}{x + 3}} \left(x + 3\right) \left(\frac{\frac{3}{2} - \frac{x}{2}}{\left(x + 3\right)^{2}} + \frac{1}{2 x + 6}\right)}{x - 3}$$
________
/ -3 + x / 1 -3 + x \
/ ------ *(3 + x)*|------- - ----------|
\/ 3 + x |6 + 2*x 2|
\ 2*(3 + x) /
-------------------------------------------
-3 + x
$$\frac{\sqrt{\frac{x - 3}{x + 3}} \left(x + 3\right) \left(- \frac{x - 3}{2 \left(x + 3\right)^{2}} + \frac{1}{2 x + 6}\right)}{x - 3}$$
sqrt((-3 + x)/(3 + x))*(3 + x)*(1/(6 + 2*x) - (-3 + x)/(2*(3 + x)^2))/(-3 + x)