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Least common denominator (x-1)*(1/(2*(x-1))-(x+1)/(2*(x-1)^2))/(x+1)

An expression to simplify:

The solution

You have entered [src]
        /    1         x + 1   \
(x - 1)*|--------- - ----------|
        |2*(x - 1)            2|
        \            2*(x - 1) /
--------------------------------
             x + 1              
$$\frac{\left(x - 1\right) \left(- \frac{x + 1}{2 \left(x - 1\right)^{2}} + \frac{1}{2 \left(x - 1\right)}\right)}{x + 1}$$
((x - 1)*(1/(2*(x - 1)) - (x + 1)/(2*(x - 1)^2)))/(x + 1)
Fraction decomposition [src]
1/(2*(1 + x)) - 1/(2*(-1 + x))
$$\frac{1}{2 \left(x + 1\right)} - \frac{1}{2 \left(x - 1\right)}$$
    1           1     
--------- - ----------
2*(1 + x)   2*(-1 + x)
General simplification [src]
  -1   
-------
      2
-1 + x 
$$- \frac{1}{x^{2} - 1}$$
-1/(-1 + x^2)
Common denominator [src]
  -1   
-------
      2
-1 + x 
$$- \frac{1}{x^{2} - 1}$$
-1/(-1 + x^2)
Rational denominator [src]
          2                      
2*(-1 + x)  + (-1 - x)*(-2 + 2*x)
---------------------------------
  2*(1 + x)*(-1 + x)*(-2 + 2*x)  
$$\frac{\left(- x - 1\right) \left(2 x - 2\right) + 2 \left(x - 1\right)^{2}}{2 \left(x - 1\right) \left(x + 1\right) \left(2 x - 2\right)}$$
(2*(-1 + x)^2 + (-1 - x)*(-2 + 2*x))/(2*(1 + x)*(-1 + x)*(-2 + 2*x))
Trigonometric part [src]
         /   1          1 + x   \
(-1 + x)*|-------- - -----------|
         |-2 + 2*x             2|
         \           2*(-1 + x) /
---------------------------------
              1 + x              
$$\frac{\left(x - 1\right) \left(\frac{1}{2 x - 2} - \frac{x + 1}{2 \left(x - 1\right)^{2}}\right)}{x + 1}$$
(-1 + x)*(1/(-2 + 2*x) - (1 + x)/(2*(-1 + x)^2))/(1 + x)
Combinatorics [src]
      -1        
----------------
(1 + x)*(-1 + x)
$$- \frac{1}{\left(x - 1\right) \left(x + 1\right)}$$
-1/((1 + x)*(-1 + x))
Powers [src]
         /              1   x \
         |            - - - - |
         |   1          2   2 |
(-1 + x)*|-------- + ---------|
         |-2 + 2*x           2|
         \           (-1 + x) /
-------------------------------
             1 + x             
$$\frac{\left(x - 1\right) \left(\frac{- \frac{x}{2} - \frac{1}{2}}{\left(x - 1\right)^{2}} + \frac{1}{2 x - 2}\right)}{x + 1}$$
         /   1          1 + x   \
(-1 + x)*|-------- - -----------|
         |-2 + 2*x             2|
         \           2*(-1 + x) /
---------------------------------
              1 + x              
$$\frac{\left(x - 1\right) \left(\frac{1}{2 x - 2} - \frac{x + 1}{2 \left(x - 1\right)^{2}}\right)}{x + 1}$$
(-1 + x)*(1/(-2 + 2*x) - (1 + x)/(2*(-1 + x)^2))/(1 + x)
Assemble expression [src]
         /   1          1 + x   \
(-1 + x)*|-------- - -----------|
         |-2 + 2*x             2|
         \           2*(-1 + x) /
---------------------------------
              1 + x              
$$\frac{\left(x - 1\right) \left(\frac{1}{2 x - 2} - \frac{x + 1}{2 \left(x - 1\right)^{2}}\right)}{x + 1}$$
(-1 + x)*(1/(-2 + 2*x) - (1 + x)/(2*(-1 + x)^2))/(1 + x)
Expand expression [src]
        /    1         x + 1   \
(x - 1)*|--------- - ----------|
        |2*(x - 1)            2|
        \            2*(x - 1) /
--------------------------------
             x + 1              
$$\frac{\left(x - 1\right) \left(\frac{1}{2 \left(x - 1\right)} - \frac{x + 1}{2 \left(x - 1\right)^{2}}\right)}{x + 1}$$
(x - 1)*(1/(2*(x - 1)) - (x + 1)/(2*(x - 1)^2))/(x + 1)
Numerical answer [src]
(-1.0 + x)*(1/(-2.0 + 2.0*x) - 0.5*(1.0 + x)/(-1.0 + x)^2)/(1.0 + x)
(-1.0 + x)*(1/(-2.0 + 2.0*x) - 0.5*(1.0 + x)/(-1.0 + x)^2)/(1.0 + x)
Combining rational expressions [src]
      -1        
----------------
(1 + x)*(-1 + x)
$$- \frac{1}{\left(x - 1\right) \left(x + 1\right)}$$
-1/((1 + x)*(-1 + x))
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