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Simplificación de expresiones/ Descomposición en fracciones simples/ asin(x/(sqrt(2)*|x-1|)-sqrt(2)/|x-1|)

¿Cómo vas a descomponer esta asin(x/(sqrt(2)*|x-1|)-sqrt(2)/|x-1|) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /                   ___ \
    |      x          \/ 2  |
asin|------------- - -------|
    |  ___           |x - 1||
    \\/ 2 *|x - 1|          /
$$\operatorname{asin}{\left(\frac{x}{\sqrt{2} \left|{x - 1}\right|} - \frac{\sqrt{2}}{\left|{x - 1}\right|} \right)}$$ 
asin(x/((sqrt(2)*|x - 1|)) - sqrt(2)/|x - 1|)
Descomposición de una fracción [src] 
asin(-sqrt(2)/|x - 1| + x*sqrt(2)/(2*|x - 1|))
$$\operatorname{asin}{\left(\frac{\sqrt{2} x}{2 \left|{x - 1}\right|} - \frac{\sqrt{2}}{\left|{x - 1}\right|} \right)}$$ 
    /     ___         ___ \
    |   \/ 2      x*\/ 2  |
asin|- ------- + ---------|
    \  |x - 1|   2*|x - 1|/
Simplificación general [src] 
    /  ___         \
    |\/ 2 *(-2 + x)|
asin|--------------|
    \  2*|-1 + x|  /
$$\operatorname{asin}{\left(\frac{\sqrt{2} \left(x - 2\right)}{2 \left|{x - 1}\right|} \right)}$$ 
asin(sqrt(2)*(-2 + x)/(2*|-1 + x|))
Abrimos la expresión [src] 
    /     ___         ___ \
    |   \/ 2      x*\/ 2  |
asin|- ------- + ---------|
    \  |x - 1|   2*|x - 1|/
$$\operatorname{asin}{\left(\frac{\sqrt{2} x}{2 \left|{x - 1}\right|} - \frac{\sqrt{2}}{\left|{x - 1}\right|} \right)}$$ 
asin(-sqrt(2)/|x - 1| + x*sqrt(2)/(2*|x - 1|))
Denominador racional [src] 
    /  ___         \
    |\/ 2 *(-2 + x)|
asin|--------------|
    \  2*|-1 + x|  /
$$\operatorname{asin}{\left(\frac{\sqrt{2} \left(x - 2\right)}{2 \left|{x - 1}\right|} \right)}$$ 
asin(sqrt(2)*(-2 + x)/(2*|-1 + x|))
Respuesta numérica [src] 
asin(x/((sqrt(2)*|x - 1|)) - sqrt(2)/|x - 1|)
asin(x/((sqrt(2)*|x - 1|)) - sqrt(2)/|x - 1|)
Denominador común [src] 
    /     ___          ___  \
    |   \/ 2       x*\/ 2   |
asin|- -------- + ----------|
    \  |-1 + x|   2*|-1 + x|/
$$\operatorname{asin}{\left(\frac{\sqrt{2} x}{2 \left|{x - 1}\right|} - \frac{\sqrt{2}}{\left|{x - 1}\right|} \right)}$$ 
asin(-sqrt(2)/|-1 + x| + x*sqrt(2)/(2*|-1 + x|))
Unión de expresiones racionales [src] 
    /  ___         \
    |\/ 2 *(-2 + x)|
asin|--------------|
    \  2*|-1 + x|  /
$$\operatorname{asin}{\left(\frac{\sqrt{2} \left(x - 2\right)}{2 \left|{x - 1}\right|} \right)}$$ 
asin(sqrt(2)*(-2 + x)/(2*|-1 + x|))
Combinatoria [src] 
    /     ___          ___  \
    |   \/ 2       x*\/ 2   |
asin|- -------- + ----------|
    \  |-1 + x|   2*|-1 + x|/
$$\operatorname{asin}{\left(\frac{\sqrt{2} x}{2 \left|{x - 1}\right|} - \frac{\sqrt{2}}{\left|{x - 1}\right|} \right)}$$ 
asin(-sqrt(2)/|-1 + x| + x*sqrt(2)/(2*|-1 + x|))
Potencias [src] 
    /     ___          ___  \
    |   \/ 2       x*\/ 2   |
asin|- -------- + ----------|
    \  |-1 + x|   2*|-1 + x|/
$$\operatorname{asin}{\left(\frac{\sqrt{2} x}{2 \left|{x - 1}\right|} - \frac{\sqrt{2}}{\left|{x - 1}\right|} \right)}$$ 
asin(-sqrt(2)/|-1 + x| + x*sqrt(2)/(2*|-1 + x|))
Parte trigonométrica [src] 
    /     ___          ___  \
    |   \/ 2       x*\/ 2   |
asin|- -------- + ----------|
    \  |-1 + x|   2*|-1 + x|/
$$\operatorname{asin}{\left(\frac{\sqrt{2} x}{2 \left|{x - 1}\right|} - \frac{\sqrt{2}}{\left|{x - 1}\right|} \right)}$$ 
asin(-sqrt(2)/|-1 + x| + x*sqrt(2)/(2*|-1 + x|))
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