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