Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(3п/2+а)1/(a*x-1)-1/(a*x+1)

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   /3*pi    \          
cos|---- + a|          
   \ 2      /      1   
------------- - -------
   a*x - 1      a*x + 1
−1ax+1+cos⁡(a+3π2)ax−1- \frac{1}{a x + 1} + \frac{\cos{\left(a + \frac{3 \pi}{2} \right)}}{a x - 1} 
cos((3*pi)/2 + a)/(a*x - 1) - 1/(a*x + 1)
Simplificación general [src] 
1 + (1 + a*x)*sin(a) - a*x
--------------------------
   (1 + a*x)*(-1 + a*x)
−ax+(ax+1)sin⁡(a)+1(ax−1)(ax+1)\frac{- a x + \left(a x + 1\right) \sin{\left(a \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 + (1 + a*x)*sin(a) - a*x)/((1 + a*x)*(-1 + a*x))
Denominador común [src] 
1 - a*x + a*x*sin(a) + sin(a)
-----------------------------
                2  2         
          -1 + a *x
axsin⁡(a)−ax+sin⁡(a)+1a2x2−1\frac{a x \sin{\left(a \right)} - a x + \sin{\left(a \right)} + 1}{a^{2} x^{2} - 1} 
(1 - a*x + a*x*sin(a) + sin(a))/(-1 + a^2*x^2)
Potencias [src] 
     1       sin(a) 
- ------- + --------
  1 + a*x   -1 + a*x
−1ax+1+sin⁡(a)ax−1- \frac{1}{a x + 1} + \frac{\sin{\left(a \right)}}{a x - 1} 
               /    3*pi\      /     3*pi\
             I*|a + ----|    I*|-a - ----|
               \     2  /      \      2  /
            e               e             
            ------------- + --------------
     1            2               2       
- ------- + ------------------------------
  1 + a*x              -1 + a*x
−1ax+1+ei(−a−3π2)2+ei(a+3π2)2ax−1- \frac{1}{a x + 1} + \frac{\frac{e^{i \left(- a - \frac{3 \pi}{2}\right)}}{2} + \frac{e^{i \left(a + \frac{3 \pi}{2}\right)}}{2}}{a x - 1} 
-1/(1 + a*x) + (exp(i*(a + 3*pi/2))/2 + exp(i*(-a - 3*pi/2))/2)/(-1 + a*x)
Denominador racional [src] 
1 - a*x + a*x*sin(a) + sin(a)
-----------------------------
     (1 + a*x)*(-1 + a*x)
axsin⁡(a)−ax+sin⁡(a)+1(ax−1)(ax+1)\frac{a x \sin{\left(a \right)} - a x + \sin{\left(a \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 - a*x + a*x*sin(a) + sin(a))/((1 + a*x)*(-1 + a*x))
Unión de expresiones racionales [src] 
                 /2*a + 3*pi\      
1 + (1 + a*x)*cos|----------| - a*x
                 \    2     /      
-----------------------------------
        (1 + a*x)*(-1 + a*x)
−ax+(ax+1)cos⁡(2a+3π2)+1(ax−1)(ax+1)\frac{- a x + \left(a x + 1\right) \cos{\left(\frac{2 a + 3 \pi}{2} \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 + (1 + a*x)*cos((2*a + 3*pi)/2) - a*x)/((1 + a*x)*(-1 + a*x))
Combinatoria [src] 
1 - a*x + a*x*sin(a) + sin(a)
-----------------------------
     (1 + a*x)*(-1 + a*x)
axsin⁡(a)−ax+sin⁡(a)+1(ax−1)(ax+1)\frac{a x \sin{\left(a \right)} - a x + \sin{\left(a \right)} + 1}{\left(a x - 1\right) \left(a x + 1\right)} 
(1 - a*x + a*x*sin(a) + sin(a))/((1 + a*x)*(-1 + a*x))
Abrimos la expresión [src] 
     1       sin(a)
- ------- + -------
  a*x + 1   a*x - 1
−1ax+1+sin⁡(a)ax−1- \frac{1}{a x + 1} + \frac{\sin{\left(a \right)}}{a x - 1} 
-1/(a*x + 1) + sin(a)/(a*x - 1)
Respuesta numérica [src] 
-1/(1.0 + a*x) + cos((3*pi)/2 + a)/(-1.0 + a*x)
-1/(1.0 + a*x) + cos((3*pi)/2 + a)/(-1.0 + a*x)
Parte trigonométrica [src] 
               /    pi\
            cos|a - --|
     1         \    2 /
- ------- + -----------
  1 + a*x     -1 + a*x
−1ax+1+cos⁡(a−π2)ax−1- \frac{1}{a x + 1} + \frac{\cos{\left(a - \frac{\pi}{2} \right)}}{a x - 1} 
                               /           /a\ \
                               |      2*cot|-| |
            /       2/a   pi\\ |           \2/ |
            |1 - cot |- + --||*|1 + -----------|
            \        \2   4 // |           2/a\|
                               |    1 + cot |-||
     1                         \            \2//
- ------- + ------------------------------------
  1 + a*x               2*(-1 + a*x)
(1+2cot⁡(a2)cot⁡2(a2)+1)(1−cot⁡2(a2+π4))2(ax−1)−1ax+1\frac{\left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(1 - \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right)}{2 \left(a x - 1\right)} - \frac{1}{a x + 1} 
                         /        2/a   pi\ \
                         |     csc |- + --| |
            /      1   \ |         \2   4 / |
            |1 + ------|*|1 - --------------|
            \    csc(a)/ |       2/  a   pi\|
                         |    csc |- - + --||
     1                   \        \  2   4 //
- ------- + ---------------------------------
  1 + a*x              2*(-1 + a*x)
(1−csc⁡2(a2+π4)csc⁡2(−a2+π4))(1+1csc⁡(a))2(ax−1)−1ax+1\frac{\left(1 - \frac{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{1}{\csc{\left(a \right)}}\right)}{2 \left(a x - 1\right)} - \frac{1}{a x + 1} 
                            1            
                   1 - ------------      
                          2/a   pi\      
                       tan |- + --|      
     1                     \2   4 /      
- ------- + -----------------------------
  1 + a*x   /         1      \           
            |1 + ------------|*(-1 + a*x)
            |       2/a   pi\|           
            |    tan |- + --||           
            \        \2   4 //
1−1tan⁡2(a2+π4)(1+1tan⁡2(a2+π4))(ax−1)−1ax+1\frac{1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(a x - 1\right)} - \frac{1}{a x + 1} 
     1              1        
- ------- + -----------------
  1 + a*x   (-1 + a*x)*csc(a)
−1ax+1+1(ax−1)csc⁡(a)- \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \csc{\left(a \right)}} 
            /       2/a   pi\\             
            |1 - cot |- + --||*(1 + sin(a))
     1      \        \2   4 //             
- ------- + -------------------------------
  1 + a*x             2*(-1 + a*x)
(1−cot⁡2(a2+π4))(sin⁡(a)+1)2(ax−1)−1ax+1\frac{\left(1 - \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right) \left(\sin{\left(a \right)} + 1\right)}{2 \left(a x - 1\right)} - \frac{1}{a x + 1} 
     1      sin(a + 2*pi)
- ------- + -------------
  1 + a*x      -1 + a*x
−1ax+1+sin⁡(a+2π)ax−1- \frac{1}{a x + 1} + \frac{\sin{\left(a + 2 \pi \right)}}{a x - 1} 
                         /a\        
                    2*tan|-|        
     1                   \2/        
- ------- + ------------------------
  1 + a*x   /       2/a\\           
            |1 + tan |-||*(-1 + a*x)
            \        \2//
−1ax+1+2tan⁡(a2)(ax−1)(tan⁡2(a2)+1)- \frac{1}{a x + 1} + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)} 
                          2/a   pi\      
                  -1 + tan |- + --|      
     1                     \2   4 /      
- ------- + -----------------------------
  1 + a*x   /       2/a   pi\\           
            |1 + tan |- + --||*(-1 + a*x)
            \        \2   4 //
−1ax+1+tan⁡2(a2+π4)−1(ax−1)(tan⁡2(a2+π4)+1)- \frac{1}{a x + 1} + \frac{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1}{\left(a x - 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} 
     1                1           
- ------- + ----------------------
  1 + a*x                 /    pi\
            (-1 + a*x)*sec|a - --|
                          \    2 /
−1ax+1+1(ax−1)sec⁡(a−π2)- \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \sec{\left(a - \frac{\pi}{2} \right)}} 
     1                1           
- ------- + ----------------------
  1 + a*x                 /pi    \
            (-1 + a*x)*sec|-- - a|
                          \2     /
−1ax+1+1(ax−1)sec⁡(−a+π2)- \frac{1}{a x + 1} + \frac{1}{\left(a x - 1\right) \sec{\left(- a + \frac{\pi}{2} \right)}} 
                            1            
                  -1 + ------------      
                          2/a   pi\      
                       cot |- + --|      
     1                     \2   4 /      
- ------- + -----------------------------
  1 + a*x   /         1      \           
            |1 + ------------|*(-1 + a*x)
            |       2/a   pi\|           
            |    cot |- + --||           
            \        \2   4 //
−1+1cot⁡2(a2+π4)(1+1cot⁡2(a2+π4))(ax−1)−1ax+1\frac{-1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(a x - 1\right)} - \frac{1}{a x + 1} 
                         /a\        
                    2*cot|-|        
     1                   \2/        
- ------- + ------------------------
  1 + a*x   /       2/a\\           
            |1 + cot |-||*(-1 + a*x)
            \        \2//
−1ax+1+2cot⁡(a2)(ax−1)(cot⁡2(a2)+1)- \frac{1}{a x + 1} + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\left(a x - 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)} 
                          2/a   pi\      
                   1 - cot |- + --|      
     1                     \2   4 /      
- ------- + -----------------------------
  1 + a*x   /       2/a   pi\\           
            |1 + cot |- + --||*(-1 + a*x)
            \        \2   4 //
1−cot⁡2(a2+π4)(ax−1)(cot⁡2(a2+π4)+1)−1ax+1\frac{1 - \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(a x - 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)} - \frac{1}{a x + 1} 
     1       sin(a) 
- ------- + --------
  1 + a*x   -1 + a*x
−1ax+1+sin⁡(a)ax−1- \frac{1}{a x + 1} + \frac{\sin{\left(a \right)}}{a x - 1} 
            /          2       \             
            |       cos (a)    |             
            |1 - --------------|*(1 + sin(a))
            |         4/a   pi\|             
            |    4*sin |- + --||             
     1      \          \2   4 //             
- ------- + ---------------------------------
  1 + a*x              2*(-1 + a*x)
(1−cos⁡2(a)4sin⁡4(a2+π4))(sin⁡(a)+1)2(ax−1)−1ax+1\frac{\left(1 - \frac{\cos^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(\sin{\left(a \right)} + 1\right)}{2 \left(a x - 1\right)} - \frac{1}{a x + 1} 
                               /           /a\ \
                               |      2*tan|-| |
            /         1      \ |           \2/ |
            |1 - ------------|*|1 + -----------|
            |       2/a   pi\| |           2/a\|
            |    tan |- + --|| |    1 + tan |-||
     1      \        \2   4 // \            \2//
- ------- + ------------------------------------
  1 + a*x               2*(-1 + a*x)
(1+2tan⁡(a2)tan⁡2(a2)+1)(1−1tan⁡2(a2+π4))2(ax−1)−1ax+1\frac{\left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)}{2 \left(a x - 1\right)} - \frac{1}{a x + 1} 
            /       2/a   pi\\                  
            |    cos |- + --||                  
            |        \2   4 /| /       /    pi\\
            |1 - ------------|*|1 + cos|a - --||
            |       2/a   pi\| \       \    2 //
            |    cos |- - --||                  
     1      \        \2   4 //                  
- ------- + ------------------------------------
  1 + a*x               2*(-1 + a*x)
(1−cos⁡2(a2+π4)cos⁡2(a2−π4))(cos⁡(a−π2)+1)2(ax−1)−1ax+1\frac{\left(1 - \frac{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}\right) \left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right)}{2 \left(a x - 1\right)} - \frac{1}{a x + 1} 
     1       sin(a)
- ------- + -------
  a*x + 1   a*x - 1
−1ax+1+sin⁡(a)ax−1- \frac{1}{a x + 1} + \frac{\sin{\left(a \right)}}{a x - 1} 
            /         1      \             
            |1 - ------------|*(1 + sin(a))
            |       2/a   pi\|             
            |    tan |- + --||             
     1      \        \2   4 //             
- ------- + -------------------------------
  1 + a*x             2*(-1 + a*x)
(1−1tan⁡2(a2+π4))(sin⁡(a)+1)2(ax−1)−1ax+1\frac{\left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(\sin{\left(a \right)} + 1\right)}{2 \left(a x - 1\right)} - \frac{1}{a x + 1} 
                              /       2/a   pi\\
                              |    sec |- - --||
            /         1     \ |        \2   4 /|
            |1 + -----------|*|1 - ------------|
            |       /    pi\| |       2/a   pi\|
            |    sec|a - --|| |    sec |- + --||
     1      \       \    2 // \        \2   4 //
- ------- + ------------------------------------
  1 + a*x               2*(-1 + a*x)
(1+1sec⁡(a−π2))(−sec⁡2(a2−π4)sec⁡2(a2+π4)+1)2(ax−1)−1ax+1\frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \left(- \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right)}{2 \left(a x - 1\right)} - \frac{1}{a x + 1} 
-1/(1 + a*x) + (1 + 1/sec(a - pi/2))*(1 - sec(a/2 - pi/4)^2/sec(a/2 + pi/4)^2)/(2*(-1 + a*x))
    © Sr Examen – Калькулятор