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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(a)^(2)-sin(1)/(a*x-1)-1/(a*x+1)

¿Cómo vas a descomponer esta tan(a)^(2)-sin(1)/(a*x-1)-1/(a*x+1) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   2       sin(1)      1   
tan (a) - ------- - -------
          a*x - 1   a*x + 1
(tan⁡2(a)−sin⁡(1)ax−1)−1ax+1\left(\tan^{2}{\left(a \right)} - \frac{\sin{\left(1 \right)}}{a x - 1}\right) - \frac{1}{a x + 1} 
tan(a)^2 - sin(1)/(a*x - 1) - 1/(a*x + 1)
Simplificación general [src] 
   2         1       sin(1) 
tan (a) - ------- - --------
          1 + a*x   -1 + a*x
tan⁡2(a)−1ax+1−sin⁡(1)ax−1\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1} 
tan(a)^2 - 1/(1 + a*x) - sin(1)/(-1 + a*x)
Respuesta numérica [src] 
tan(a)^2 - 1/(1.0 + a*x) - 0.841470984807897/(-1.0 + a*x)
tan(a)^2 - 1/(1.0 + a*x) - 0.841470984807897/(-1.0 + a*x)
Denominador racional [src] 
              /             2              \      
1 + (1 + a*x)*\-sin(1) + tan (a)*(-1 + a*x)/ - a*x
--------------------------------------------------
               (1 + a*x)*(-1 + a*x)
−ax+(ax+1)((ax−1)tan⁡2(a)−sin⁡(1))+1(ax−1)(ax+1)\frac{- a x + \left(a x + 1\right) \left(\left(a x - 1\right) \tan^{2}{\left(a \right)} - \sin{\left(1 \right)}\right) + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 + (1 + a*x)*(-sin(1) + tan(a)^2*(-1 + a*x)) - a*x)/((1 + a*x)*(-1 + a*x))
Unión de expresiones racionales [src] 
              /             2              \      
1 + (1 + a*x)*\-sin(1) + tan (a)*(-1 + a*x)/ - a*x
--------------------------------------------------
               (1 + a*x)*(-1 + a*x)
−ax+(ax+1)((ax−1)tan⁡2(a)−sin⁡(1))+1(ax−1)(ax+1)\frac{- a x + \left(a x + 1\right) \left(\left(a x - 1\right) \tan^{2}{\left(a \right)} - \sin{\left(1 \right)}\right) + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 + (1 + a*x)*(-sin(1) + tan(a)^2*(-1 + a*x)) - a*x)/((1 + a*x)*(-1 + a*x))
Denominador común [src] 
   2      -1 + a*x + a*x*sin(1) + sin(1)
tan (a) - ------------------------------
                          2  2          
                    -1 + a *x
tan⁡2(a)−axsin⁡(1)+ax−1+sin⁡(1)a2x2−1\tan^{2}{\left(a \right)} - \frac{a x \sin{\left(1 \right)} + a x - 1 + \sin{\left(1 \right)}}{a^{2} x^{2} - 1} 
tan(a)^2 - (-1 + a*x + a*x*sin(1) + sin(1))/(-1 + a^2*x^2)
Potencias [src] 
   2         1       sin(1) 
tan (a) - ------- - --------
          1 + a*x   -1 + a*x
tan⁡2(a)−1ax+1−sin⁡(1)ax−1\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1} 
                            2                 
            /   I*a    -I*a\      /   -I    I\
     1      \- e    + e    /    I*\- e   + e /
- ------- - ----------------- + --------------
  1 + a*x                  2     2*(-1 + a*x) 
             / I*a    -I*a\                   
             \e    + e    /
−(−eia+e−ia)2(eia+e−ia)2−1ax+1+i(−e−i+ei)2(ax−1)- \frac{\left(- e^{i a} + e^{- i a}\right)^{2}}{\left(e^{i a} + e^{- i a}\right)^{2}} - \frac{1}{a x + 1} + \frac{i \left(- e^{- i} + e^{i}\right)}{2 \left(a x - 1\right)} 
-1/(1 + a*x) - (-exp(i*a) + exp(-i*a))^2/(exp(i*a) + exp(-i*a))^2 + i*(-exp(-i) + exp(i))/(2*(-1 + a*x))
Compilar la expresión [src] 
   2         1       sin(1) 
tan (a) - ------- - --------
          1 + a*x   -1 + a*x
tan⁡2(a)−1ax+1−sin⁡(1)ax−1\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1} 
tan(a)^2 - 1/(1 + a*x) - sin(1)/(-1 + a*x)
Combinatoria [src] 
       2                      2  2    2                
1 - tan (a) - sin(1) - a*x + a *x *tan (a) - a*x*sin(1)
-------------------------------------------------------
                  (1 + a*x)*(-1 + a*x)
a2x2tan⁡2(a)−ax−axsin⁡(1)−tan⁡2(a)−sin⁡(1)+1(ax−1)(ax+1)\frac{a^{2} x^{2} \tan^{2}{\left(a \right)} - a x - a x \sin{\left(1 \right)} - \tan^{2}{\left(a \right)} - \sin{\left(1 \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 - tan(a)^2 - sin(1) - a*x + a^2*x^2*tan(a)^2 - a*x*sin(1))/((1 + a*x)*(-1 + a*x))
Parte trigonométrica [src] 
   2         1       sin(1) 
tan (a) - ------- - --------
          1 + a*x   -1 + a*x
tan⁡2(a)−1ax+1−sin⁡(1)ax−1\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1} 
   2         1       sin(1)
tan (a) - ------- - -------
          a*x + 1   a*x - 1
tan⁡2(a)−1ax+1−sin⁡(1)ax−1\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1} 
               2/pi    \                    
            csc |-- - a|                    
     1          \2     /           1        
- ------- + ------------ - -----------------
  1 + a*x        2         (-1 + a*x)*csc(1)
              csc (a)
csc⁡2(−a+π2)csc⁡2(a)−1ax+1−1(ax−1)csc⁡(1)\frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{1}{\left(a x - 1\right) \csc{\left(1 \right)}} 
   2         1              2*tan(1/2)        
tan (a) - ------- - --------------------------
          1 + a*x   /       2     \           
                    \1 + tan (1/2)/*(-1 + a*x)
tan⁡2(a)−1ax+1−2tan⁡(12)(ax−1)(tan⁡2(12)+1)\tan^{2}{\left(a \right)} - \frac{1}{a x + 1} - \frac{2 \tan{\left(\frac{1}{2} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{1}{2} \right)} + 1\right)} 
   1         1              2*cot(1/2)        
------- - ------- - --------------------------
   2      1 + a*x   /       2     \           
cot (a)             \1 + cot (1/2)/*(-1 + a*x)
1cot⁡2(a)−1ax+1−2cot⁡(12)(1+cot⁡2(12))(ax−1)\frac{1}{\cot^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{2 \cot{\left(\frac{1}{2} \right)}}{\left(1 + \cot^{2}{\left(\frac{1}{2} \right)}\right) \left(a x - 1\right)} 
                            4   
     1       sin(1)    4*sin (a)
- ------- - -------- + ---------
  1 + a*x   -1 + a*x      2     
                       sin (2*a)
4sin⁡4(a)sin⁡2(2a)−1ax+1−sin⁡(1)ax−1\frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1} 
               2              
     1      sin (a)    sin(1) 
- ------- + ------- - --------
  1 + a*x      2      -1 + a*x
            cos (a)
sin⁡2(a)cos⁡2(a)−1ax+1−sin⁡(1)ax−1\frac{\sin^{2}{\left(a \right)}}{\cos^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{\sin{\left(1 \right)}}{a x - 1} 
               2                       
     1      sec (a)           1        
- ------- + ------- - -----------------
  1 + a*x      2      (-1 + a*x)*csc(1)
            csc (a)
sec⁡2(a)csc⁡2(a)−1ax+1−1(ax−1)csc⁡(1)\frac{\sec^{2}{\left(a \right)}}{\csc^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{1}{\left(a x - 1\right) \csc{\left(1 \right)}} 
                 2                               
     1        sec (a)                1           
- ------- + ------------ - ----------------------
  1 + a*x      2/    pi\                 /    pi\
            sec |a - --|   (-1 + a*x)*sec|1 - --|
                \    2 /                 \    2 /
sec⁡2(a)sec⁡2(a−π2)−1ax+1−1(ax−1)sec⁡(1−π2)\frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{1}{a x + 1} - \frac{1}{\left(a x - 1\right) \sec{\left(1 - \frac{\pi}{2} \right)}} 
               2/    pi\      /    pi\
            cos |a - --|   cos|1 - --|
     1          \    2 /      \    2 /
- ------- + ------------ - -----------
  1 + a*x        2           -1 + a*x 
              cos (a)
cos⁡2(a−π2)cos⁡2(a)−1ax+1−cos⁡(1−π2)ax−1\frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}} - \frac{1}{a x + 1} - \frac{\cos{\left(1 - \frac{\pi}{2} \right)}}{a x - 1} 
-1/(1 + a*x) + cos(a - pi/2)^2/cos(a)^2 - cos(1 - pi/2)/(-1 + a*x)
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