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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   /       2     \
cot\1 - cos (3)*x/
------------------
      2           
     x  + 5*x
cot⁡(−xcos⁡2(3)+1)x2+5x\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)
Simplificación general [src] 
    /          2   \ 
-cot\-1 + x*cos (3)/ 
---------------------
      x*(5 + x)
−cot⁡(xcos⁡2(3)−1)x(x+5)- \frac{\cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x \left(x + 5\right)} 
-cot(-1 + x*cos(3)^2)/(x*(5 + x))
Respuesta numérica [src] 
cot(1 - cos(3)^2*x)/(x^2 + 5.0*x)
cot(1 - cos(3)^2*x)/(x^2 + 5.0*x)
Potencias [src] 
    /          2   \ 
-cot\-1 + x*cos (3)/ 
---------------------
        2            
       x  + 5*x
−cot⁡(xcos⁡2(3)−1)x2+5x- \frac{\cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x^{2} + 5 x} 
    /                     2\ 
    |       / -3*I    3*I\ | 
    |       |e       e   | | 
-cot|-1 + x*|----- + ----| | 
    \       \  2      2  / / 
-----------------------------
            2                
           x  + 5*x
−cot⁡(x(e−3i2+e3i2)2−1)x2+5x- \frac{\cot{\left(x \left(\frac{e^{- 3 i}}{2} + \frac{e^{3 i}}{2}\right)^{2} - 1 \right)}}{x^{2} + 5 x} 
-cot(-1 + x*(exp(-3*i)/2 + exp(3*i)/2)^2)/(x^2 + 5*x)
Combinatoria [src] 
    /          2   \ 
-cot\-1 + x*cos (3)/ 
---------------------
      x*(5 + x)
−cot⁡(xcos⁡2(3)−1)x(x+5)- \frac{\cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x \left(x + 5\right)} 
-cot(-1 + x*cos(3)^2)/(x*(5 + x))
Unión de expresiones racionales [src] 
    /          2   \ 
-cot\-1 + x*cos (3)/ 
---------------------
      x*(5 + x)
−cot⁡(xcos⁡2(3)−1)x(x+5)- \frac{\cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x \left(x + 5\right)} 
-cot(-1 + x*cos(3)^2)/(x*(5 + x))
Denominador racional [src] 
    /          2   \ 
-cot\-1 + x*cos (3)/ 
---------------------
      x*(5 + x)
−cot⁡(xcos⁡2(3)−1)x(x+5)- \frac{\cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x \left(x + 5\right)} 
-cot(-1 + x*cos(3)^2)/(x*(5 + x))
Denominador común [src] 
    /          2   \ 
-cot\-1 + x*cos (3)/ 
---------------------
        2            
       x  + 5*x
−cot⁡(xcos⁡2(3)−1)x2+5x- \frac{\cot{\left(x \cos^{2}{\left(3 \right)} - 1 \right)}}{x^{2} + 5 x} 
-cot(-1 + x*cos(3)^2)/(x^2 + 5*x)
Abrimos la expresión [src] 
    /             4             2              6   \ 
-cot\-1 - 24*x*cos (1) + 9*x*cos (1) + 16*x*cos (1)/ 
-----------------------------------------------------
                        2                            
                       x  + 5*x
−cot⁡(−24xcos⁡4(1)+16xcos⁡6(1)+9xcos⁡2(1)−1)x2+5x- \frac{\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} 
-cot(-1 - 24*x*cos(1)^4 + 9*x*cos(1)^2 + 16*x*cos(1)^6)/(x^2 + 5*x)
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