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

An expression to simplify:

The solution

You have entered [src]
  2 - 2*x                      
 e               2      2 - 2*x
---------- + ---------*e       
         2   2*(x - 1)         
2*(x - 1)                      
$$\frac{2}{2 \left(x - 1\right)} e^{2 - 2 x} + \frac{e^{2 - 2 x}}{2 \left(x - 1\right)^{2}}$$
exp(2 - 2*x)/((2*(x - 1)^2)) + (2/((2*(x - 1))))*exp(2 - 2*x)
General simplification [src]
            2 - 2*x
(-1/2 + x)*e       
-------------------
             2     
     (-1 + x)      
$$\frac{\left(x - \frac{1}{2}\right) e^{2 - 2 x}}{\left(x - 1\right)^{2}}$$
(-1/2 + x)*exp(2 - 2*x)/(-1 + x)^2
Numerical answer [src]
0.5*exp(2 - 2*x)/(-1.0 + x)^2 + 2.0*exp(2 - 2*x)/(-2.0 + 2.0*x)
0.5*exp(2 - 2*x)/(-1.0 + x)^2 + 2.0*exp(2 - 2*x)/(-2.0 + 2.0*x)
Powers [src]
   2 - 2*x       2 - 2*x
  e           2*e       
----------- + ----------
          2    -2 + 2*x 
2*(-1 + x)              
$$\frac{2 e^{2 - 2 x}}{2 x - 2} + \frac{e^{2 - 2 x}}{2 \left(x - 1\right)^{2}}$$
exp(2 - 2*x)/(2*(-1 + x)^2) + 2*exp(2 - 2*x)/(-2 + 2*x)
Common denominator [src]
           2        2        
        - e  + 2*x*e         
-----------------------------
   2*x        2*x      2  2*x
2*e    - 4*x*e    + 2*x *e   
$$\frac{2 x e^{2} - e^{2}}{2 x^{2} e^{2 x} - 4 x e^{2 x} + 2 e^{2 x}}$$
(-exp(2) + 2*x*exp(2))/(2*exp(2*x) - 4*x*exp(2*x) + 2*x^2*exp(2*x))
Assemble expression [src]
   2 - 2*x       2 - 2*x
  e           2*e       
----------- + ----------
          2    -2 + 2*x 
2*(-1 + x)              
$$\frac{2 e^{2 - 2 x}}{2 x - 2} + \frac{e^{2 - 2 x}}{2 \left(x - 1\right)^{2}}$$
exp(2 - 2*x)/(2*(-1 + x)^2) + 2*exp(2 - 2*x)/(-2 + 2*x)
Expand expression [src]
 2 - 2*x     2 - 2*x 
e           e        
-------- + ----------
 x - 1              2
           2*(x - 1) 
$$\frac{e^{2 - 2 x}}{x - 1} + \frac{e^{2 - 2 x}}{2 \left(x - 1\right)^{2}}$$
exp(2 - 2*x)/(x - 1) + exp(2 - 2*x)/(2*(x - 1)^2)
Rational denominator [src]
            2 - 2*x             2  2 - 2*x
(-2 + 2*x)*e        + 4*(-1 + x) *e       
------------------------------------------
                    2                     
          2*(-1 + x) *(-2 + 2*x)          
$$\frac{4 \left(x - 1\right)^{2} e^{2 - 2 x} + \left(2 x - 2\right) e^{2 - 2 x}}{2 \left(x - 1\right)^{2} \left(2 x - 2\right)}$$
((-2 + 2*x)*exp(2 - 2*x) + 4*(-1 + x)^2*exp(2 - 2*x))/(2*(-1 + x)^2*(-2 + 2*x))
Combining rational expressions [src]
            2 - 2*x
(-1 + 2*x)*e       
-------------------
              2    
    2*(-1 + x)     
$$\frac{\left(2 x - 1\right) e^{2 - 2 x}}{2 \left(x - 1\right)^{2}}$$
(-1 + 2*x)*exp(2 - 2*x)/(2*(-1 + x)^2)
Combinatorics [src]
            2  -2*x
(-1 + 2*x)*e *e    
-------------------
              2    
    2*(-1 + x)     
$$\frac{\left(2 x - 1\right) e^{2} e^{- 2 x}}{2 \left(x - 1\right)^{2}}$$
(-1 + 2*x)*exp(2)*exp(-2*x)/(2*(-1 + x)^2)
Trigonometric part [src]
 /cosh(-2 + 2*x)   sinh(-2 + 2*x)                                      \ 
-|-------------- - -------------- + x*sinh(-2 + 2*x) - x*cosh(-2 + 2*x)| 
 \      2                2                                             / 
-------------------------------------------------------------------------
                                        2                                
                                (-1 + x)                                 
$$- \frac{x \sinh{\left(2 x - 2 \right)} - x \cosh{\left(2 x - 2 \right)} - \frac{\sinh{\left(2 x - 2 \right)}}{2} + \frac{\cosh{\left(2 x - 2 \right)}}{2}}{\left(x - 1\right)^{2}}$$
   2 - 2*x       2 - 2*x
  e           2*e       
----------- + ----------
          2    -2 + 2*x 
2*(-1 + x)              
$$\frac{2 e^{2 - 2 x}}{2 x - 2} + \frac{e^{2 - 2 x}}{2 \left(x - 1\right)^{2}}$$
cosh(2 - 2*x) + sinh(2 - 2*x)   2*(cosh(2 - 2*x) + sinh(2 - 2*x))
----------------------------- + ---------------------------------
                   2                         -2 + 2*x            
         2*(-1 + x)                                              
$$\frac{2 \left(\sinh{\left(2 - 2 x \right)} + \cosh{\left(2 - 2 x \right)}\right)}{2 x - 2} + \frac{\sinh{\left(2 - 2 x \right)} + \cosh{\left(2 - 2 x \right)}}{2 \left(x - 1\right)^{2}}$$
(cosh(2 - 2*x) + sinh(2 - 2*x))/(2*(-1 + x)^2) + 2*(cosh(2 - 2*x) + sinh(2 - 2*x))/(-2 + 2*x)