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Simplificación de expresiones/ Descomposición en fracciones simples/ ctg(1-cos^2*3*x)/(x^2+5*x)oo

¿Cómo vas a descomponer esta ctg(1-cos^2*3*x)/(x^2+5*x)oo expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /       2     \   
cot\1 - cos (3)*x/   
------------------*oo
      2              
     x  + 5*x
$$\infty \frac{\cot{\left(- x \cos^{2}{\left(3 \right)} + 1 \right)}}{x^{2} + 5 x}$$ 
(cot(1 - cos(3)^2*x)/(x^2 + 5*x))*oo
Respuesta numérica [src] 
oo*cot(1 - cos(3)^2*x)/(x^2 + 5.0*x)
oo*cot(1 - cos(3)^2*x)/(x^2 + 5.0*x)
Denominador común [src] 
       /          2   \
-oo*cot\-1 + x*cos (3)/
-----------------------
         2             
        x  + 5*x
$$- \frac{\infty \cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x^{2} + 5 x}$$ 
-oo*cot(-1 + x*cos(3)^2)/(x^2 + 5*x)
Denominador racional [src] 
       /          2   \
-oo*cot\-1 + x*cos (3)/
-----------------------
       x*(5 + x)
$$- \frac{\infty \cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x \left(x + 5\right)}$$ 
-oo*cot(-1 + x*cos(3)^2)/(x*(5 + x))
Combinatoria [src] 
       /          2   \
-oo*cot\-1 + x*cos (3)/
-----------------------
       x*(5 + x)
$$- \frac{\infty \cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x \left(x + 5\right)}$$ 
-oo*cot(-1 + x*cos(3)^2)/(x*(5 + x))
Potencias [src] 
       /                     2\
       |       / -3*I    3*I\ |
       |       |e       e   | |
-oo*cot|-1 + x*|----- + ----| |
       \       \  2      2  / /
-------------------------------
             2                 
            x  + 5*x
$$- \frac{\infty \cot{\left(x \left(\frac{e^{- 3 i}}{2} + \frac{e^{3 i}}{2}\right)^{2} - 1 \right)}}{x^{2} + 5 x}$$ 
       /          2   \
-oo*cot\-1 + x*cos (3)/
-----------------------
         2             
        x  + 5*x
$$- \frac{\infty \cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x^{2} + 5 x}$$ 
-oo*cot(-1 + x*cos(3)^2)/(x^2 + 5*x)
Abrimos la expresión [src] 
       /             4             2              6   \
-oo*cot\-1 - 24*x*cos (1) + 9*x*cos (1) + 16*x*cos (1)/
-------------------------------------------------------
                         2                             
                        x  + 5*x
$$- \frac{\infty \cot{\left(- 24 x \cos^{4}{\left(1 \right)} + 16 x \cos^{6}{\left(1 \right)} + 9 x \cos^{2}{\left(1 \right)} - 1 \right)}}{x^{2} + 5 x}$$ 
-oo*cot(-1 - 24*x*cos(1)^4 + 9*x*cos(1)^2 + 16*x*cos(1)^6)/(x^2 + 5*x)
Compilar la expresión [src] 
      /       2     \
oo*cot\1 - cos (3)*x/
---------------------
        2            
       x  + 5*x
$$\frac{\infty \cot{\left(- x \cos^{2}{\left(3 \right)} + 1 \right)}}{x^{2} + 5 x}$$ 
oo*cot(1 - cos(3)^2*x)/(x^2 + 5*x)
Unión de expresiones racionales [src] 
       /          2   \
-oo*cot\-1 + x*cos (3)/
-----------------------
       x*(5 + x)
$$- \frac{\infty \cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x \left(x + 5\right)}$$ 
-oo*cot(-1 + x*cos(3)^2)/(x*(5 + x))
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