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Simplificación de expresiones/ Descomposición en fracciones simples/ asin(x/(sqrt(5)*|x-1|)-3/(sqrt(5)*|x-1|))

¿Cómo vas a descomponer esta asin(x/(sqrt(5)*|x-1|)-3/(sqrt(5)*|x-1|)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /      x               3      \
asin|------------- - -------------|
    |  ___             ___        |
    \\/ 5 *|x - 1|   \/ 5 *|x - 1|/
asin⁡(x5∣x−1∣−35∣x−1∣)\operatorname{asin}{\left(\frac{x}{\sqrt{5} \left|{x - 1}\right|} - \frac{3}{\sqrt{5} \left|{x - 1}\right|} \right)} 
asin(x/((sqrt(5)*|x - 1|)) - 3*sqrt(5)/(5*|x - 1|))
Descomposición de una fracción [src] 
asin(-3*sqrt(5)/(5*|x - 1|) + x*sqrt(5)/(5*|x - 1|))
asin⁡(5x5∣x−1∣−355∣x−1∣)\operatorname{asin}{\left(\frac{\sqrt{5} x}{5 \left|{x - 1}\right|} - \frac{3 \sqrt{5}}{5 \left|{x - 1}\right|} \right)} 
    /       ___         ___ \
    |   3*\/ 5      x*\/ 5  |
asin|- --------- + ---------|
    \  5*|x - 1|   5*|x - 1|/
Simplificación general [src] 
    /  ___         \
    |\/ 5 *(-3 + x)|
asin|--------------|
    \  5*|-1 + x|  /
asin⁡(5(x−3)5∣x−1∣)\operatorname{asin}{\left(\frac{\sqrt{5} \left(x - 3\right)}{5 \left|{x - 1}\right|} \right)} 
asin(sqrt(5)*(-3 + x)/(5*|-1 + x|))
Abrimos la expresión [src] 
    /       ___         ___ \
    |   3*\/ 5      x*\/ 5  |
asin|- --------- + ---------|
    \  5*|x - 1|   5*|x - 1|/
asin⁡(5x5∣x−1∣−355∣x−1∣)\operatorname{asin}{\left(\frac{\sqrt{5} x}{5 \left|{x - 1}\right|} - \frac{3 \sqrt{5}}{5 \left|{x - 1}\right|} \right)} 
asin(-3*sqrt(5)/(5*|x - 1|) + x*sqrt(5)/(5*|x - 1|))
Denominador racional [src] 
    /  ___         \
    |\/ 5 *(-3 + x)|
asin|--------------|
    \  5*|-1 + x|  /
asin⁡(5(x−3)5∣x−1∣)\operatorname{asin}{\left(\frac{\sqrt{5} \left(x - 3\right)}{5 \left|{x - 1}\right|} \right)} 
asin(sqrt(5)*(-3 + x)/(5*|-1 + x|))
Respuesta numérica [src] 
asin(x/((sqrt(5)*|x - 1|)) - 3*sqrt(5)/(5*|x - 1|))
asin(x/((sqrt(5)*|x - 1|)) - 3*sqrt(5)/(5*|x - 1|))
Parte trigonométrica [src] 
    /       ___          ___  \
    |   3*\/ 5       x*\/ 5   |
asin|- ---------- + ----------|
    \  5*|-1 + x|   5*|-1 + x|/
asin⁡(5x5∣x−1∣−355∣x−1∣)\operatorname{asin}{\left(\frac{\sqrt{5} x}{5 \left|{x - 1}\right|} - \frac{3 \sqrt{5}}{5 \left|{x - 1}\right|} \right)} 
asin(-3*sqrt(5)/(5*|-1 + x|) + x*sqrt(5)/(5*|-1 + x|))
Denominador común [src] 
    /       ___          ___  \
    |   3*\/ 5       x*\/ 5   |
asin|- ---------- + ----------|
    \  5*|-1 + x|   5*|-1 + x|/
asin⁡(5x5∣x−1∣−355∣x−1∣)\operatorname{asin}{\left(\frac{\sqrt{5} x}{5 \left|{x - 1}\right|} - \frac{3 \sqrt{5}}{5 \left|{x - 1}\right|} \right)} 
asin(-3*sqrt(5)/(5*|-1 + x|) + x*sqrt(5)/(5*|-1 + x|))
Combinatoria [src] 
    /       ___          ___  \
    |   3*\/ 5       x*\/ 5   |
asin|- ---------- + ----------|
    \  5*|-1 + x|   5*|-1 + x|/
asin⁡(5x5∣x−1∣−355∣x−1∣)\operatorname{asin}{\left(\frac{\sqrt{5} x}{5 \left|{x - 1}\right|} - \frac{3 \sqrt{5}}{5 \left|{x - 1}\right|} \right)} 
asin(-3*sqrt(5)/(5*|-1 + x|) + x*sqrt(5)/(5*|-1 + x|))
Potencias [src] 
    /       ___          ___  \
    |   3*\/ 5       x*\/ 5   |
asin|- ---------- + ----------|
    \  5*|-1 + x|   5*|-1 + x|/
asin⁡(5x5∣x−1∣−355∣x−1∣)\operatorname{asin}{\left(\frac{\sqrt{5} x}{5 \left|{x - 1}\right|} - \frac{3 \sqrt{5}}{5 \left|{x - 1}\right|} \right)} 
asin(-3*sqrt(5)/(5*|-1 + x|) + x*sqrt(5)/(5*|-1 + x|))
Unión de expresiones racionales [src] 
    /  ___         \
    |\/ 5 *(-3 + x)|
asin|--------------|
    \  5*|-1 + x|  /
asin⁡(5(x−3)5∣x−1∣)\operatorname{asin}{\left(\frac{\sqrt{5} \left(x - 3\right)}{5 \left|{x - 1}\right|} \right)} 
asin(sqrt(5)*(-3 + x)/(5*|-1 + x|))
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