Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt((x-9)/(x+9))*(x+9)*(1/(2*(x+9))-(x-9)/(2*(x+9)^2))/(x-9)
¿Cómo vas a descomponer esta sqrt((x-9)/(x+9))*(x+9)*(1/(2*(x+9))-(x-9)/(2*(x+9)^2))/(x-9) expresión en fracciones?
Solución
Ha introducido
[src]
_______
/ x - 9 / 1 x - 9 \
/ ----- *(x + 9)*|--------- - ----------|
\/ x + 9 |2*(x + 9) 2|
\ 2*(x + 9) /
--------------------------------------------
x - 9
$$\frac{\sqrt{\frac{x - 9}{x + 9}} \left(x + 9\right) \left(- \frac{x - 9}{2 \left(x + 9\right)^{2}} + \frac{1}{2 \left(x + 9\right)}\right)}{x - 9}$$
((sqrt((x - 9)/(x + 9))*(x + 9))*(1/(2*(x + 9)) - (x - 9)/(2*(x + 9)^2)))/(x - 9)
Simplificación general
[src]
________
/ -9 + x
9* / ------
\/ 9 + x
--------------
2
-81 + x
$$\frac{9 \sqrt{\frac{x - 9}{x + 9}}}{x^{2} - 81}$$
9*sqrt((-9 + x)/(9 + x))/(-81 + x^2)
Respuesta numérica
[src]
((-9.0 + x)/(9.0 + x))^0.5*(9.0 + x)*(1/(18.0 + 2.0*x) - 0.00617283950617284*(-9.0 + x)/(1 + 0.111111111111111*x)^2)/(-9.0 + x)
((-9.0 + x)/(9.0 + x))^0.5*(9.0 + x)*(1/(18.0 + 2.0*x) - 0.00617283950617284*(-9.0 + x)/(1 + 0.111111111111111*x)^2)/(-9.0 + x)
Compilar la expresión
[src]
________
/ -9 + x / 1 -9 + x \
/ ------ *(9 + x)*|-------- - ----------|
\/ 9 + x |18 + 2*x 2|
\ 2*(9 + x) /
--------------------------------------------
-9 + x
$$\frac{\sqrt{\frac{x - 9}{x + 9}} \left(x + 9\right) \left(- \frac{x - 9}{2 \left(x + 9\right)^{2}} + \frac{1}{2 x + 18}\right)}{x - 9}$$
sqrt((-9 + x)/(9 + x))*(9 + x)*(1/(18 + 2*x) - (-9 + x)/(2*(9 + x)^2))/(-9 + x)
Parte trigonométrica
[src]
________
/ -9 + x / 1 -9 + x \
/ ------ *(9 + x)*|-------- - ----------|
\/ 9 + x |18 + 2*x 2|
\ 2*(9 + x) /
--------------------------------------------
-9 + x
$$\frac{\sqrt{\frac{x - 9}{x + 9}} \left(x + 9\right) \left(- \frac{x - 9}{2 \left(x + 9\right)^{2}} + \frac{1}{2 x + 18}\right)}{x - 9}$$
sqrt((-9 + x)/(9 + x))*(9 + x)*(1/(18 + 2*x) - (-9 + x)/(2*(9 + x)^2))/(-9 + x)
Potencias
[src]
________
/ -9 + x / 1 -9 + x \
/ ------ *(9 + x)*|-------- - ----------|
\/ 9 + x |18 + 2*x 2|
\ 2*(9 + x) /
--------------------------------------------
-9 + x
$$\frac{\sqrt{\frac{x - 9}{x + 9}} \left(x + 9\right) \left(- \frac{x - 9}{2 \left(x + 9\right)^{2}} + \frac{1}{2 x + 18}\right)}{x - 9}$$
/ 9 x \
________ | - - - |
/ -9 + x | 1 2 2 |
/ ------ *(9 + x)*|-------- + --------|
\/ 9 + x |18 + 2*x 2|
\ (9 + x) /
------------------------------------------
-9 + x
$$\frac{\sqrt{\frac{x - 9}{x + 9}} \left(x + 9\right) \left(\frac{\frac{9}{2} - \frac{x}{2}}{\left(x + 9\right)^{2}} + \frac{1}{2 x + 18}\right)}{x - 9}$$
sqrt((-9 + x)/(9 + x))*(9 + x)*(1/(18 + 2*x) + (9/2 - x/2)/(9 + x)^2)/(-9 + x)
Combinatoria
[src]
________
/ -9 + x
9* / ------
\/ 9 + x
----------------
(-9 + x)*(9 + x)
$$\frac{9 \sqrt{\frac{x - 9}{x + 9}}}{\left(x - 9\right) \left(x + 9\right)}$$
9*sqrt((-9 + x)/(9 + x))/((-9 + x)*(9 + x))
Unión de expresiones racionales
[src]
________
/ -9 + x
9* / ------
\/ 9 + x
----------------
(-9 + x)*(9 + x)
$$\frac{9 \sqrt{\frac{x - 9}{x + 9}}}{\left(x - 9\right) \left(x + 9\right)}$$
9*sqrt((-9 + x)/(9 + x))/((-9 + x)*(9 + x))
Denominador racional
[src]
_________________ _________________ _________________
/ 9 x 2 / 9 x 2 / 9 x
162* / - ----- + ----- - 2*x * / - ----- + ----- + 2*(9 + x) * / - ----- + -----
\/ x + 9 x + 9 \/ x + 9 x + 9 \/ x + 9 x + 9
-----------------------------------------------------------------------------------------
2*(-9 + x)*(9 + x)*(18 + 2*x)
$$\frac{- 2 x^{2} \sqrt{\frac{x}{x + 9} - \frac{9}{x + 9}} + 2 \left(x + 9\right)^{2} \sqrt{\frac{x}{x + 9} - \frac{9}{x + 9}} + 162 \sqrt{\frac{x}{x + 9} - \frac{9}{x + 9}}}{2 \left(x - 9\right) \left(x + 9\right) \left(2 x + 18\right)}$$
(162*sqrt(-9/(x + 9) + x/(x + 9)) - 2*x^2*sqrt(-9/(x + 9) + x/(x + 9)) + 2*(9 + x)^2*sqrt(-9/(x + 9) + x/(x + 9)))/(2*(-9 + x)*(9 + x)*(18 + 2*x))
Denominador común
[src]
_________________
/ 9 x
9* / - ----- + -----
\/ 9 + x 9 + x
-----------------------
2
-81 + x
$$\frac{9 \sqrt{\frac{x}{x + 9} - \frac{9}{x + 9}}}{x^{2} - 81}$$
9*sqrt(-9/(9 + x) + x/(9 + x))/(-81 + x^2)