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
$$\frac{\frac{\sqrt{x - 2}}{x + 2} + \frac{\sqrt{x + 2}}{x - 2}}{- \frac{\sqrt{x - 2}}{x + 2} + \frac{\sqrt{x + 2}}{x - 2}}$$
(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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/ 3/2 3/2\
-\(-2 + x) + (2 + x) /
----------------------------
3/2 3/2
(-2 + x) - (2 + x)
$$- \frac{\left(x - 2\right)^{\frac{3}{2}} + \left(x + 2\right)^{\frac{3}{2}}}{\left(x - 2\right)^{\frac{3}{2}} - \left(x + 2\right)^{\frac{3}{2}}}$$
-((-2 + x)^(3/2) + (2 + x)^(3/2))/((-2 + x)^(3/2) - (2 + x)^(3/2))
Respuesta numérica
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(1.4142135623731*(1 + 0.5*x)^0.5/(-2.0 + x) + 1.4142135623731*(-1 + 0.5*x)^0.5/(2.0 + x))/(1.4142135623731*(1 + 0.5*x)^0.5/(-2.0 + x) - 1.4142135623731*(-1 + 0.5*x)^0.5/(2.0 + x))
(1.4142135623731*(1 + 0.5*x)^0.5/(-2.0 + x) + 1.4142135623731*(-1 + 0.5*x)^0.5/(2.0 + x))/(1.4142135623731*(1 + 0.5*x)^0.5/(-2.0 + x) - 1.4142135623731*(-1 + 0.5*x)^0.5/(2.0 + x))
Denominador común
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________ ________
- 4*\/ -2 + x + 2*x*\/ -2 + x
1 + -------------------------------------------------------
________ _______ _______ ________
2*\/ -2 + x + 2*\/ 2 + x + x*\/ 2 + x - x*\/ -2 + x
$$\frac{2 x \sqrt{x - 2} - 4 \sqrt{x - 2}}{- x \sqrt{x - 2} + x \sqrt{x + 2} + 2 \sqrt{x - 2} + 2 \sqrt{x + 2}} + 1$$
1 + (-4*sqrt(-2 + x) + 2*x*sqrt(-2 + x))/(2*sqrt(-2 + x) + 2*sqrt(2 + x) + x*sqrt(2 + x) - x*sqrt(-2 + x))
Unión de expresiones racionales
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3/2 3/2
(-2 + x) + (2 + x)
------------------------
3/2 3/2
(2 + x) - (-2 + x)
$$\frac{\left(x - 2\right)^{\frac{3}{2}} + \left(x + 2\right)^{\frac{3}{2}}}{- \left(x - 2\right)^{\frac{3}{2}} + \left(x + 2\right)^{\frac{3}{2}}}$$
((-2 + x)^(3/2) + (2 + x)^(3/2))/((2 + x)^(3/2) - (-2 + x)^(3/2))
Denominador racional
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2
/ 3/2 3/2\
\(-2 + x) + (2 + x) /
---------------------------
2
16 + 12*x
$$\frac{\left(\left(x - 2\right)^{\frac{3}{2}} + \left(x + 2\right)^{\frac{3}{2}}\right)^{2}}{12 x^{2} + 16}$$
((-2 + x)^(3/2) + (2 + x)^(3/2))^2/(16 + 12*x^2)
Combinatoria
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________ _______ ________ _______
- 2*\/ -2 + x + 2*\/ 2 + x + x*\/ -2 + x + x*\/ 2 + x
---------------------------------------------------------
________ _______ _______ ________
2*\/ -2 + x + 2*\/ 2 + x + x*\/ 2 + x - x*\/ -2 + x
$$\frac{x \sqrt{x - 2} + x \sqrt{x + 2} - 2 \sqrt{x - 2} + 2 \sqrt{x + 2}}{- x \sqrt{x - 2} + x \sqrt{x + 2} + 2 \sqrt{x - 2} + 2 \sqrt{x + 2}}$$
(-2*sqrt(-2 + x) + 2*sqrt(2 + x) + x*sqrt(-2 + x) + x*sqrt(2 + x))/(2*sqrt(-2 + x) + 2*sqrt(2 + x) + x*sqrt(2 + x) - x*sqrt(-2 + x))