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Simplificación de expresiones/ Descomposición en fracciones simples/ Ctg1/(a*x-1)-1/(a*x+1)

¿Cómo vas a descomponer esta Ctg1/(a*x-1)-1/(a*x+1) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
 cot(1)      1   
------- - -------
a*x - 1   a*x + 1
−1ax+1+cot⁡(1)ax−1- \frac{1}{a x + 1} + \frac{\cot{\left(1 \right)}}{a x - 1} 
cot(1)/(a*x - 1) - 1/(a*x + 1)
Simplificación general [src] 
1 + (1 + a*x)*cot(1) - a*x
--------------------------
   (1 + a*x)*(-1 + a*x)
−ax+(ax+1)cot⁡(1)+1(ax−1)(ax+1)\frac{- a x + \left(a x + 1\right) \cot{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 + (1 + a*x)*cot(1) - a*x)/((1 + a*x)*(-1 + a*x))
Respuesta numérica [src] 
-1/(1.0 + a*x) + 0.642092615934331/(-1.0 + a*x)
-1/(1.0 + a*x) + 0.642092615934331/(-1.0 + a*x)
Combinatoria [src] 
1 - a*x + a*x*cot(1) + cot(1)
-----------------------------
     (1 + a*x)*(-1 + a*x)
−ax+axcot⁡(1)+cot⁡(1)+1(ax−1)(ax+1)\frac{- a x + a x \cot{\left(1 \right)} + \cot{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 - a*x + a*x*cot(1) + cot(1))/((1 + a*x)*(-1 + a*x))
Denominador común [src] 
1 - a*x + a*x*cot(1) + cot(1)
-----------------------------
                2  2         
          -1 + a *x
−ax+axcot⁡(1)+cot⁡(1)+1a2x2−1\frac{- a x + a x \cot{\left(1 \right)} + \cot{\left(1 \right)} + 1}{a^{2} x^{2} - 1} 
(1 - a*x + a*x*cot(1) + cot(1))/(-1 + a^2*x^2)
Unión de expresiones racionales [src] 
1 + (1 + a*x)*cot(1) - a*x
--------------------------
   (1 + a*x)*(-1 + a*x)
−ax+(ax+1)cot⁡(1)+1(ax−1)(ax+1)\frac{- a x + \left(a x + 1\right) \cot{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 + (1 + a*x)*cot(1) - a*x)/((1 + a*x)*(-1 + a*x))
Parte trigonométrica [src] 
     1               csc(1)        
- ------- + -----------------------
  1 + a*x                 /     pi\
            (-1 + a*x)*csc|-1 + --|
                          \     2 /
−1ax+1+csc⁡(1)(ax−1)csc⁡(−1+π2)- \frac{1}{a x + 1} + \frac{\csc{\left(1 \right)}}{\left(a x - 1\right) \csc{\left(-1 + \frac{\pi}{2} \right)}} 
     1            csc(1)     
- ------- + -----------------
  1 + a*x   (-1 + a*x)*sec(1)
−1ax+1+csc⁡(1)(ax−1)sec⁡(1)- \frac{1}{a x + 1} + \frac{\csc{\left(1 \right)}}{\left(a x - 1\right) \sec{\left(1 \right)}} 
                  /    pi\   
               sec|1 - --|   
     1            \    2 /   
- ------- + -----------------
  1 + a*x   (-1 + a*x)*sec(1)
−1ax+1+sec⁡(1−π2)(ax−1)sec⁡(1)- \frac{1}{a x + 1} + \frac{\sec{\left(1 - \frac{\pi}{2} \right)}}{\left(a x - 1\right) \sec{\left(1 \right)}} 
     1             sin(2)       
- ------- + --------------------
  1 + a*x                   2   
            2*(-1 + a*x)*sin (1)
−1ax+1+sin⁡(2)2(ax−1)sin⁡2(1)- \frac{1}{a x + 1} + \frac{\sin{\left(2 \right)}}{2 \left(a x - 1\right) \sin^{2}{\left(1 \right)}} 
     1              cos(1)        
- ------- + ----------------------
  1 + a*x                 /    pi\
            (-1 + a*x)*cos|1 - --|
                          \    2 /
−1ax+1+cos⁡(1)(ax−1)cos⁡(1−π2)- \frac{1}{a x + 1} + \frac{\cos{\left(1 \right)}}{\left(a x - 1\right) \cos{\left(1 - \frac{\pi}{2} \right)}} 
     1              1        
- ------- + -----------------
  1 + a*x   (-1 + a*x)*tan(1)
−1ax+1+1(ax−1)tan⁡(1)- \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \tan{\left(1 \right)}} 
     1            cos(1)     
- ------- + -----------------
  1 + a*x   (-1 + a*x)*sin(1)
−1ax+1+cos⁡(1)(ax−1)sin⁡(1)- \frac{1}{a x + 1} + \frac{\cos{\left(1 \right)}}{\left(a x - 1\right) \sin{\left(1 \right)}} 
-1/(1 + a*x) + cos(1)/((-1 + a*x)*sin(1))
Denominador racional [src] 
1 + (1 + a*x)*cot(1) - a*x
--------------------------
   (1 + a*x)*(-1 + a*x)
−ax+(ax+1)cot⁡(1)+1(ax−1)(ax+1)\frac{- a x + \left(a x + 1\right) \cot{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 + (1 + a*x)*cot(1) - a*x)/((1 + a*x)*(-1 + a*x))
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