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Simplificación de expresiones/ Descomposición en fracciones simples/ |((sqrt(x)+sqrt(2a))^2)/((sqrt(2x)+sqrt(a))^2)|

¿Cómo vas a descomponer esta |((sqrt(x)+sqrt(2a))^2)/((sqrt(2x)+sqrt(a))^2)| expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
|                 2|
|/  ___     _____\ |
|\\/ x  + \/ 2*a / |
|------------------|
|                 2|
|/  _____     ___\ |
|\\/ 2*x  + \/ a / |
∣(x+2a)2(a+2x)2∣\left|{\frac{\left(\sqrt{x} + \sqrt{2 a}\right)^{2}}{\left(\sqrt{a} + \sqrt{2 x}\right)^{2}}}\right| 
Abs((sqrt(x) + sqrt(2*a))^2/(sqrt(2*x) + sqrt(a))^2)
Descomposición de una fracción [src] 
Abs(x/(a + 2*x + 2*sqrt(a)*(sqrt(2)*sqrt(x))) + 2*a/(a + 2*x + 2*sqrt(a)*(sqrt(2)*sqrt(x))) + 2*sqrt(2)*sqrt(a)*sqrt(x)/(a + 2*x + 2*sqrt(a)*(sqrt(2)*sqrt(x))))
∣22ax2a2x+a+2x+2a2a2x+a+2x+x2a2x+a+2x∣\left|{\frac{2 \sqrt{2} \sqrt{a} \sqrt{x}}{2 \sqrt{a} \sqrt{2} \sqrt{x} + a + 2 x} + \frac{2 a}{2 \sqrt{a} \sqrt{2} \sqrt{x} + a + 2 x} + \frac{x}{2 \sqrt{a} \sqrt{2} \sqrt{x} + a + 2 x}}\right| 
|                                                                         ___   ___   ___     |
|              x                              2*a                     2*\/ 2 *\/ a *\/ x      |
|----------------------------- + ----------------------------- + -----------------------------|
|              ___   ___   ___                 ___   ___   ___                 ___   ___   ___|
|a + 2*x + 2*\/ a *\/ 2 *\/ x    a + 2*x + 2*\/ a *\/ 2 *\/ x    a + 2*x + 2*\/ a *\/ 2 *\/ x |
Simplificación general [src] 
|                     2|
|/  ___     ___   ___\ |
|\\/ x  + \/ 2 *\/ a / |
|----------------------|
|                     2|
|/  ___     ___   ___\ |
|\\/ a  + \/ 2 *\/ x / |
∣(2a+x)2(a+2x)2∣\left|{\frac{\left(\sqrt{2} \sqrt{a} + \sqrt{x}\right)^{2}}{\left(\sqrt{a} + \sqrt{2} \sqrt{x}\right)^{2}}}\right| 
Abs((sqrt(x) + sqrt(2)*sqrt(a))^2/(sqrt(a) + sqrt(2)*sqrt(x))^2)
Abrimos la expresión [src] 
|                     2|
|/  ___     ___   ___\ |
|\\/ x  + \/ 2 *\/ a / |
|----------------------|
|                     2|
|/  ___     ___   ___\ |
|\\/ a  + \/ 2 *\/ x / |
∣(2a+x)2(a+2x)2∣\left|{\frac{\left(\sqrt{2} \sqrt{a} + \sqrt{x}\right)^{2}}{\left(\sqrt{a} + \sqrt{2} \sqrt{x}\right)^{2}}}\right| 
Abs((sqrt(x) + sqrt(2)*sqrt(a))^2/(sqrt(a) + sqrt(2)*sqrt(x))^2)
Respuesta numérica [src] 
Abs((sqrt(x) + sqrt(2*a))^2/(sqrt(2*x) + sqrt(a))^2)
Abs((sqrt(x) + sqrt(2*a))^2/(sqrt(2*x) + sqrt(a))^2)
Unión de expresiones racionales [src] 
|                     2|
|/  ___     ___   ___\ |
|\\/ x  + \/ 2 *\/ a / |
|----------------------|
|                     2|
|/  ___     ___   ___\ |
|\\/ a  + \/ 2 *\/ x / |
∣(2a+x)2(a+2x)2∣\left|{\frac{\left(\sqrt{2} \sqrt{a} + \sqrt{x}\right)^{2}}{\left(\sqrt{a} + \sqrt{2} \sqrt{x}\right)^{2}}}\right| 
Abs((sqrt(x) + sqrt(2)*sqrt(a))^2/(sqrt(a) + sqrt(2)*sqrt(x))^2)
Denominador racional [src] 
|                     2                      2|
|/  ___     ___   ___\  /  ___     ___   ___\ |
|\\/ a  - \/ 2 *\/ x / *\\/ x  + \/ 2 *\/ a / |
|---------------------------------------------|
|                           2                 |
|                  (a - 2*x)                  |
∣(a−2x)2(2a+x)2(a−2x)2∣\left|{\frac{\left(\sqrt{a} - \sqrt{2} \sqrt{x}\right)^{2} \left(\sqrt{2} \sqrt{a} + \sqrt{x}\right)^{2}}{\left(a - 2 x\right)^{2}}}\right| 
Abs((sqrt(a) - sqrt(2)*sqrt(x))^2*(sqrt(x) + sqrt(2)*sqrt(a))^2/(a - 2*x)^2)
Denominador común [src] 
|                                                                         ___   ___   ___     |
|              x                              2*a                     2*\/ 2 *\/ a *\/ x      |
|----------------------------- + ----------------------------- + -----------------------------|
|              ___   ___   ___                 ___   ___   ___                 ___   ___   ___|
|a + 2*x + 2*\/ 2 *\/ a *\/ x    a + 2*x + 2*\/ 2 *\/ a *\/ x    a + 2*x + 2*\/ 2 *\/ a *\/ x |
∣22ax22ax+a+2x+2a22ax+a+2x+x22ax+a+2x∣\left|{\frac{2 \sqrt{2} \sqrt{a} \sqrt{x}}{2 \sqrt{2} \sqrt{a} \sqrt{x} + a + 2 x} + \frac{2 a}{2 \sqrt{2} \sqrt{a} \sqrt{x} + a + 2 x} + \frac{x}{2 \sqrt{2} \sqrt{a} \sqrt{x} + a + 2 x}}\right| 
Abs(x/(a + 2*x + 2*sqrt(2)*sqrt(a)*sqrt(x)) + 2*a/(a + 2*x + 2*sqrt(2)*sqrt(a)*sqrt(x)) + 2*sqrt(2)*sqrt(a)*sqrt(x)/(a + 2*x + 2*sqrt(2)*sqrt(a)*sqrt(x)))
Parte trigonométrica [src] 
|                     2|
|/  ___     ___   ___\ |
|\\/ x  + \/ 2 *\/ a / |
|----------------------|
|                     2|
|/  ___     ___   ___\ |
|\\/ a  + \/ 2 *\/ x / |
∣(2a+x)2(a+2x)2∣\left|{\frac{\left(\sqrt{2} \sqrt{a} + \sqrt{x}\right)^{2}}{\left(\sqrt{a} + \sqrt{2} \sqrt{x}\right)^{2}}}\right| 
Abs((sqrt(x) + sqrt(2)*sqrt(a))^2/(sqrt(a) + sqrt(2)*sqrt(x))^2)
Potencias [src] 
|                     2|
|/  ___     ___   ___\ |
|\\/ x  + \/ 2 *\/ a / |
|----------------------|
|                     2|
|/  ___     ___   ___\ |
|\\/ a  + \/ 2 *\/ x / |
∣(2a+x)2(a+2x)2∣\left|{\frac{\left(\sqrt{2} \sqrt{a} + \sqrt{x}\right)^{2}}{\left(\sqrt{a} + \sqrt{2} \sqrt{x}\right)^{2}}}\right| 
Abs((sqrt(x) + sqrt(2)*sqrt(a))^2/(sqrt(a) + sqrt(2)*sqrt(x))^2)
Combinatoria [src] 
|                                                                         ___   ___   ___     |
|              x                              2*a                     2*\/ 2 *\/ a *\/ x      |
|----------------------------- + ----------------------------- + -----------------------------|
|              ___   ___   ___                 ___   ___   ___                 ___   ___   ___|
|a + 2*x + 2*\/ 2 *\/ a *\/ x    a + 2*x + 2*\/ 2 *\/ a *\/ x    a + 2*x + 2*\/ 2 *\/ a *\/ x |
∣22ax22ax+a+2x+2a22ax+a+2x+x22ax+a+2x∣\left|{\frac{2 \sqrt{2} \sqrt{a} \sqrt{x}}{2 \sqrt{2} \sqrt{a} \sqrt{x} + a + 2 x} + \frac{2 a}{2 \sqrt{2} \sqrt{a} \sqrt{x} + a + 2 x} + \frac{x}{2 \sqrt{2} \sqrt{a} \sqrt{x} + a + 2 x}}\right| 
Abs(x/(a + 2*x + 2*sqrt(2)*sqrt(a)*sqrt(x)) + 2*a/(a + 2*x + 2*sqrt(2)*sqrt(a)*sqrt(x)) + 2*sqrt(2)*sqrt(a)*sqrt(x)/(a + 2*x + 2*sqrt(2)*sqrt(a)*sqrt(x)))
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