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Simplificación de expresiones/ Descomposición en fracciones simples/ -x+sin(4*x)/(4*cos(4*x))

¿Cómo vas a descomponer esta -x+sin(4*x)/(4*cos(4*x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
      sin(4*x) 
-x + ----------
     4*cos(4*x)
$$- x + \frac{\sin{\left(4 x \right)}}{4 \cos{\left(4 x \right)}}$$ 
-x + sin(4*x)/((4*cos(4*x)))
Simplificación general [src] 
     tan(4*x)
-x + --------
        4
$$- x + \frac{\tan{\left(4 x \right)}}{4}$$ 
-x + tan(4*x)/4
Respuesta numérica [src] 
-x + 0.25*sin(4*x)/cos(4*x)
-x + 0.25*sin(4*x)/cos(4*x)
Combinatoria [src] 
-(-sin(4*x) + 4*x*cos(4*x)) 
----------------------------
         4*cos(4*x)
$$- \frac{4 x \cos{\left(4 x \right)} - \sin{\left(4 x \right)}}{4 \cos{\left(4 x \right)}}$$ 
-(-sin(4*x) + 4*x*cos(4*x))/(4*cos(4*x))
Potencias [src] 
        /   -4*I*x    4*I*x\ 
      I*\- e       + e     / 
-x - ------------------------
       /   -4*I*x      4*I*x\
     2*\2*e       + 2*e     /
$$- x - \frac{i \left(e^{4 i x} - e^{- 4 i x}\right)}{2 \left(2 e^{4 i x} + 2 e^{- 4 i x}\right)}$$ 
-x - i*(-exp(-4*i*x) + exp(4*i*x))/(2*(2*exp(-4*i*x) + 2*exp(4*i*x)))
Unión de expresiones racionales [src] 
-4*x*cos(4*x) + sin(4*x)
------------------------
       4*cos(4*x)
$$\frac{- 4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{4 \cos{\left(4 x \right)}}$$ 
(-4*x*cos(4*x) + sin(4*x))/(4*cos(4*x))
Denominador racional [src] 
-4*x*cos(4*x) + sin(4*x)
------------------------
       4*cos(4*x)
$$\frac{- 4 x \cos{\left(4 x \right)} + \sin{\left(4 x \right)}}{4 \cos{\left(4 x \right)}}$$ 
(-4*x*cos(4*x) + sin(4*x))/(4*cos(4*x))
Abrimos la expresión [src] 
                                           3              
           cos(x)*sin(x)              2*sin (x)*cos(x)    
-x + ------------------------- - -------------------------
              2           4               2           4   
     1 - 8*cos (x) + 8*cos (x)   1 - 8*cos (x) + 8*cos (x)
$$- x - \frac{2 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 8 \cos^{2}{\left(x \right)} + 1} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{8 \cos^{4}{\left(x \right)} - 8 \cos^{2}{\left(x \right)} + 1}$$ 
-x + cos(x)*sin(x)/(1 - 8*cos(x)^2 + 8*cos(x)^4) - 2*sin(x)^3*cos(x)/(1 - 8*cos(x)^2 + 8*cos(x)^4)
Parte trigonométrica [src] 
        /pi      \
     csc|-- - 4*x|
        \2       /
-x + -------------
       4*csc(4*x)
$$- x + \frac{\csc{\left(- 4 x + \frac{\pi}{2} \right)}}{4 \csc{\left(4 x \right)}}$$ 
          tan(2*x)    
-x + -----------------
       /       2     \
     2*\1 - tan (2*x)/
$$- x + \frac{\tan{\left(2 x \right)}}{2 \left(1 - \tan^{2}{\left(2 x \right)}\right)}$$ 
        /      pi\
     cos|4*x - --|
        \      2 /
-x + -------------
       4*cos(4*x)
$$- x + \frac{\cos{\left(4 x - \frac{\pi}{2} \right)}}{4 \cos{\left(4 x \right)}}$$ 
          cot(2*x)     
-x + ------------------
       /        2     \
     2*\-1 + cot (2*x)/
$$- x + \frac{\cot{\left(2 x \right)}}{2 \left(\cot^{2}{\left(2 x \right)} - 1\right)}$$ 
      sec(4*x) 
-x + ----------
     4*csc(4*x)
$$- x + \frac{\sec{\left(4 x \right)}}{4 \csc{\left(4 x \right)}}$$ 
     tan(4*x)
-x + --------
        4
$$- x + \frac{\tan{\left(4 x \right)}}{4}$$ 
         1     
-x + ----------
     4*cot(4*x)
$$- x + \frac{1}{4 \cot{\left(4 x \right)}}$$ 
         sec(4*x)   
-x + ---------------
          /      pi\
     4*sec|4*x - --|
          \      2 /
$$- x + \frac{\sec{\left(4 x \right)}}{4 \sec{\left(4 x - \frac{\pi}{2} \right)}}$$ 
        2      
     sin (4*x) 
-x + ----------
     2*sin(8*x)
$$- x + \frac{\sin^{2}{\left(4 x \right)}}{2 \sin{\left(8 x \right)}}$$ 
         sin(4*x)   
-x + ---------------
          /pi      \
     4*sin|-- + 4*x|
          \2       /
$$- x + \frac{\sin{\left(4 x \right)}}{4 \sin{\left(4 x + \frac{\pi}{2} \right)}}$$ 
-x + sin(4*x)/(4*sin(pi/2 + 4*x))
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