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Simplificación de expresiones/ Descomposición en fracciones simples/ log(x-5*x^2)/(2*sqrt(x+2))+sqrt(x+2)*(1-10*x)/(x-5*x^2)

¿Cómo vas a descomponer esta log(x-5*x^2)/(2*sqrt(x+2))+sqrt(x+2)*(1-10*x)/(x-5*x^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /       2\     _______           
log\x - 5*x /   \/ x + 2 *(1 - 10*x)
------------- + --------------------
     _______                 2      
 2*\/ x + 2           x - 5*x
$$\frac{\left(1 - 10 x\right) \sqrt{x + 2}}{- 5 x^{2} + x} + \frac{\log{\left(- 5 x^{2} + x \right)}}{2 \sqrt{x + 2}}$$ 
log(x - 5*x^2)/((2*sqrt(x + 2))) + (sqrt(x + 2)*(1 - 10*x))/(x - 5*x^2)
Simplificación general [src] 
                      x*(-1 + 5*x)*log(x*(1 - 5*x))
(-1 + 10*x)*(2 + x) + -----------------------------
                                    2              
---------------------------------------------------
                              _______              
               x*(-1 + 5*x)*\/ 2 + x
$$\frac{\frac{x \left(5 x - 1\right) \log{\left(x \left(1 - 5 x\right) \right)}}{2} + \left(x + 2\right) \left(10 x - 1\right)}{x \sqrt{x + 2} \left(5 x - 1\right)}$$ 
((-1 + 10*x)*(2 + x) + x*(-1 + 5*x)*log(x*(1 - 5*x))/2)/(x*(-1 + 5*x)*sqrt(2 + x))
Denominador racional [src] 
         2               /       2\      2    /       2\
-4 + 20*x  + 38*x - x*log\x - 5*x / + 5*x *log\x - 5*x /
--------------------------------------------------------
                    _______ /        2\                 
                2*\/ 2 + x *\-x + 5*x /
$$\frac{5 x^{2} \log{\left(- 5 x^{2} + x \right)} + 20 x^{2} - x \log{\left(- 5 x^{2} + x \right)} + 38 x - 4}{2 \sqrt{x + 2} \left(5 x^{2} - x\right)}$$ 
(-4 + 20*x^2 + 38*x - x*log(x - 5*x^2) + 5*x^2*log(x - 5*x^2))/(2*sqrt(2 + x)*(-x + 5*x^2))
Respuesta numérica [src] 
0.353553390593274*(1 + 0.5*x)^(-0.5)*log(x - 5*x^2) + 1.4142135623731*(1 + 0.5*x)^0.5*(1.0 - 10.0*x)/(x - 5.0*x^2)
0.353553390593274*(1 + 0.5*x)^(-0.5)*log(x - 5*x^2) + 1.4142135623731*(1 + 0.5*x)^0.5*(1.0 - 10.0*x)/(x - 5.0*x^2)
Combinatoria [src] 
         2               /       2\      2    /       2\
-4 + 20*x  + 38*x - x*log\x - 5*x / + 5*x *log\x - 5*x /
--------------------------------------------------------
                                 _______                
                2*x*(-1 + 5*x)*\/ 2 + x
$$\frac{5 x^{2} \log{\left(- 5 x^{2} + x \right)} + 20 x^{2} - x \log{\left(- 5 x^{2} + x \right)} + 38 x - 4}{2 x \sqrt{x + 2} \left(5 x - 1\right)}$$ 
(-4 + 20*x^2 + 38*x - x*log(x - 5*x^2) + 5*x^2*log(x - 5*x^2))/(2*x*(-1 + 5*x)*sqrt(2 + x))
Denominador común [src] 
         2               /       2\      2    /       2\
-4 + 20*x  + 38*x - x*log\x - 5*x / + 5*x *log\x - 5*x /
--------------------------------------------------------
                   _______       2   _______            
           - 2*x*\/ 2 + x  + 10*x *\/ 2 + x
$$\frac{5 x^{2} \log{\left(- 5 x^{2} + x \right)} + 20 x^{2} - x \log{\left(- 5 x^{2} + x \right)} + 38 x - 4}{10 x^{2} \sqrt{x + 2} - 2 x \sqrt{x + 2}}$$ 
(-4 + 20*x^2 + 38*x - x*log(x - 5*x^2) + 5*x^2*log(x - 5*x^2))/(-2*x*sqrt(2 + x) + 10*x^2*sqrt(2 + x))
Unión de expresiones racionales [src] 
2*(1 - 10*x)*(2 + x) + x*(1 - 5*x)*log(x*(1 - 5*x))
---------------------------------------------------
                              _______              
              2*x*(1 - 5*x)*\/ 2 + x
$$\frac{x \left(1 - 5 x\right) \log{\left(x \left(1 - 5 x\right) \right)} + 2 \left(1 - 10 x\right) \left(x + 2\right)}{2 x \left(1 - 5 x\right) \sqrt{x + 2}}$$ 
(2*(1 - 10*x)*(2 + x) + x*(1 - 5*x)*log(x*(1 - 5*x)))/(2*x*(1 - 5*x)*sqrt(2 + x))
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