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Simplificación de expresiones/ Descomposición en fracciones simples/ asin(x/(sqrt(6)*|x+2|)+7/(sqrt(6)*|x+2|))/5^(3/2)+sqrt(x^2+2*x-5)/(10+5*x)

¿Cómo vas a descomponer esta asin(x/(sqrt(6)*|x+2|)+7/(sqrt(6)*|x+2|))/5^(3/2)+sqrt(x^2+2*x-5)/(10+5*x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
    /      x               7      \                    
asin|------------- + -------------|      ______________
    |  ___             ___        |     /  2           
    \\/ 6 *|x + 2|   \/ 6 *|x + 2|/   \/  x  + 2*x - 5 
----------------------------------- + -----------------
                 3/2                       10 + 5*x    
                5
$$\frac{\operatorname{asin}{\left(\frac{x}{\sqrt{6} \left|{x + 2}\right|} + \frac{7}{\sqrt{6} \left|{x + 2}\right|} \right)}}{5^{\frac{3}{2}}} + \frac{\sqrt{\left(x^{2} + 2 x\right) - 5}}{5 x + 10}$$ 
asin(x/((sqrt(6)*|x + 2|)) + 7/((sqrt(6)*|x + 2|)))/5^(3/2) + sqrt(x^2 + 2*x - 5)/(10 + 5*x)
Simplificación general [src] 
     _______________                     /  ___        \
    /       2            ___             |\/ 6 *(7 + x)|
5*\/  -5 + x  + 2*x  + \/ 5 *(2 + x)*asin|-------------|
                                         \  6*|2 + x|  /
--------------------------------------------------------
                       25*(2 + x)
$$\frac{\sqrt{5} \left(x + 2\right) \operatorname{asin}{\left(\frac{\sqrt{6} \left(x + 7\right)}{6 \left|{x + 2}\right|} \right)} + 5 \sqrt{x^{2} + 2 x - 5}}{25 \left(x + 2\right)}$$ 
(5*sqrt(-5 + x^2 + 2*x) + sqrt(5)*(2 + x)*asin(sqrt(6)*(7 + x)/(6*|2 + x|)))/(25*(2 + x))
Respuesta numérica [src] 
0.0894427190999916*asin(x/((sqrt(6)*|x + 2|)) + 7/((sqrt(6)*|x + 2|))) + 2.23606797749979*(-1 + 0.2*x^2 + 0.4*x)^0.5/(10.0 + 5.0*x)
0.0894427190999916*asin(x/((sqrt(6)*|x + 2|)) + 7/((sqrt(6)*|x + 2|))) + 2.23606797749979*(-1 + 0.2*x^2 + 0.4*x)^0.5/(10.0 + 5.0*x)
Abrimos la expresión [src] 
   ______________                                    
  /  2                ___     /     ___         ___ \
\/  x  + 2*x - 5    \/ 5      | 7*\/ 6      x*\/ 6  |
----------------- + -----*asin|--------- + ---------|
     10 + 5*x         25      \6*|x + 2|   6*|x + 2|/
$$\frac{\sqrt{5}}{25} \operatorname{asin}{\left(\frac{\sqrt{6} x}{6 \left|{x + 2}\right|} + \frac{7 \sqrt{6}}{6 \left|{x + 2}\right|} \right)} + \frac{\sqrt{\left(x^{2} + 2 x\right) - 5}}{5 x + 10}$$ 
sqrt(x^2 + 2*x - 5)/(10 + 5*x) + (sqrt(5)/25)*asin(7*sqrt(6)/(6*|x + 2|) + x*sqrt(6)/(6*|x + 2|))
Compilar la expresión [src] 
                       ___     /      x               7      \
   _______________   \/ 5 *asin|------------- + -------------|
  /       2                    |  ___             ___        |
\/  -5 + x  + 2*x              \\/ 6 *|x + 2|   \/ 6 *|x + 2|/
------------------ + -----------------------------------------
     10 + 5*x                            25
$$\frac{\sqrt{5} \operatorname{asin}{\left(\frac{x}{\sqrt{6} \left|{x + 2}\right|} + \frac{7}{\sqrt{6} \left|{x + 2}\right|} \right)}}{25} + \frac{\sqrt{x^{2} + 2 x - 5}}{5 x + 10}$$ 
sqrt(-5 + x^2 + 2*x)/(10 + 5*x) + sqrt(5)*asin(x/((sqrt(6)*|x + 2|)) + 7/((sqrt(6)*|x + 2|)))/25
Parte trigonométrica [src] 
                               /     ___         ___ \
   _______________     ___     | 7*\/ 6      x*\/ 6  |
  /       2          \/ 5 *asin|--------- + ---------|
\/  -5 + x  + 2*x              \6*|2 + x|   6*|2 + x|/
------------------ + ---------------------------------
     10 + 5*x                        25
$$\frac{\sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{6} x}{6 \left|{x + 2}\right|} + \frac{7 \sqrt{6}}{6 \left|{x + 2}\right|} \right)}}{25} + \frac{\sqrt{x^{2} + 2 x - 5}}{5 x + 10}$$ 
sqrt(-5 + x^2 + 2*x)/(10 + 5*x) + sqrt(5)*asin(7*sqrt(6)/(6*|2 + x|) + x*sqrt(6)/(6*|2 + x|))/25
Combinatoria [src] 
     _______________               /     ___         ___ \               /     ___         ___ \
    /       2              ___     | 7*\/ 6      x*\/ 6  |       ___     | 7*\/ 6      x*\/ 6  |
5*\/  -5 + x  + 2*x  + 2*\/ 5 *asin|--------- + ---------| + x*\/ 5 *asin|--------- + ---------|
                                   \6*|2 + x|   6*|2 + x|/               \6*|2 + x|   6*|2 + x|/
------------------------------------------------------------------------------------------------
                                           25*(2 + x)
$$\frac{\sqrt{5} x \operatorname{asin}{\left(\frac{\sqrt{6} x}{6 \left|{x + 2}\right|} + \frac{7 \sqrt{6}}{6 \left|{x + 2}\right|} \right)} + 5 \sqrt{x^{2} + 2 x - 5} + 2 \sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{6} x}{6 \left|{x + 2}\right|} + \frac{7 \sqrt{6}}{6 \left|{x + 2}\right|} \right)}}{25 \left(x + 2\right)}$$ 
(5*sqrt(-5 + x^2 + 2*x) + 2*sqrt(5)*asin(7*sqrt(6)/(6*|2 + x|) + x*sqrt(6)/(6*|2 + x|)) + x*sqrt(5)*asin(7*sqrt(6)/(6*|2 + x|) + x*sqrt(6)/(6*|2 + x|)))/(25*(2 + x))
Denominador común [src] 
                               /     ___         ___ \
   _______________     ___     | 7*\/ 6      x*\/ 6  |
  /       2          \/ 5 *asin|--------- + ---------|
\/  -5 + x  + 2*x              \6*|2 + x|   6*|2 + x|/
------------------ + ---------------------------------
     10 + 5*x                        25
$$\frac{\sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{6} x}{6 \left|{x + 2}\right|} + \frac{7 \sqrt{6}}{6 \left|{x + 2}\right|} \right)}}{25} + \frac{\sqrt{x^{2} + 2 x - 5}}{5 x + 10}$$ 
sqrt(-5 + x^2 + 2*x)/(10 + 5*x) + sqrt(5)*asin(7*sqrt(6)/(6*|2 + x|) + x*sqrt(6)/(6*|2 + x|))/25
Denominador racional [src] 
     _______________               /     ___         ___ \               /     ___         ___ \
    /       2              ___     | 7*\/ 6      x*\/ 6  |       ___     | 7*\/ 6      x*\/ 6  |
5*\/  -5 + x  + 2*x  + 2*\/ 5 *asin|--------- + ---------| + x*\/ 5 *asin|--------- + ---------|
                                   \6*|2 + x|   6*|2 + x|/               \6*|2 + x|   6*|2 + x|/
------------------------------------------------------------------------------------------------
                                           50 + 25*x
$$\frac{\sqrt{5} x \operatorname{asin}{\left(\frac{\sqrt{6} x}{6 \left|{x + 2}\right|} + \frac{7 \sqrt{6}}{6 \left|{x + 2}\right|} \right)} + 5 \sqrt{x^{2} + 2 x - 5} + 2 \sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{6} x}{6 \left|{x + 2}\right|} + \frac{7 \sqrt{6}}{6 \left|{x + 2}\right|} \right)}}{25 x + 50}$$ 
(5*sqrt(-5 + x^2 + 2*x) + 2*sqrt(5)*asin(7*sqrt(6)/(6*|2 + x|) + x*sqrt(6)/(6*|2 + x|)) + x*sqrt(5)*asin(7*sqrt(6)/(6*|2 + x|) + x*sqrt(6)/(6*|2 + x|)))/(50 + 25*x)
Potencias [src] 
                               /     ___         ___ \
   _______________     ___     | 7*\/ 6      x*\/ 6  |
  /       2          \/ 5 *asin|--------- + ---------|
\/  -5 + x  + 2*x              \6*|2 + x|   6*|2 + x|/
------------------ + ---------------------------------
     10 + 5*x                        25
$$\frac{\sqrt{5} \operatorname{asin}{\left(\frac{\sqrt{6} x}{6 \left|{x + 2}\right|} + \frac{7 \sqrt{6}}{6 \left|{x + 2}\right|} \right)}}{25} + \frac{\sqrt{x^{2} + 2 x - 5}}{5 x + 10}$$ 
sqrt(-5 + x^2 + 2*x)/(10 + 5*x) + sqrt(5)*asin(7*sqrt(6)/(6*|2 + x|) + x*sqrt(6)/(6*|2 + x|))/25
Unión de expresiones racionales [src] 
                                         /  ___        \
    ________________     ___             |\/ 6 *(7 + x)|
5*\/ -5 + x*(2 + x)  + \/ 5 *(2 + x)*asin|-------------|
                                         \  6*|2 + x|  /
--------------------------------------------------------
                       25*(2 + x)
$$\frac{\sqrt{5} \left(x + 2\right) \operatorname{asin}{\left(\frac{\sqrt{6} \left(x + 7\right)}{6 \left|{x + 2}\right|} \right)} + 5 \sqrt{x \left(x + 2\right) - 5}}{25 \left(x + 2\right)}$$ 
(5*sqrt(-5 + x*(2 + x)) + sqrt(5)*(2 + x)*asin(sqrt(6)*(7 + x)/(6*|2 + x|)))/(25*(2 + x))
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