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Expression simplification/ Least common denominator/ x+(6-x^2/1+x)/6+x/(x^2-1)

Least common denominator x+(6-x^2/1+x)/6+x/(x^2-1)

An expression to simplify:

The solution

You have entered [src] 
         2             
        x              
    6 - -- + x         
        1          x   
x + ---------- + ------
        6         2    
                 x  - 1
$$\frac{x}{x^{2} - 1} + \left(x + \frac{x + \left(- \frac{x^{2}}{1} + 6\right)}{6}\right)$$ 
x + (6 - x^2/1 + x)/6 + x/(x^2 - 1)
Fraction decomposition [src] 
1 + 1/(2*(1 + x)) + 1/(2*(-1 + x)) - x^2/6 + 7*x/6
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + 1 + \frac{1}{2 \left(x + 1\right)} + \frac{1}{2 \left(x - 1\right)}$$ 
                              2      
        1           1        x    7*x
1 + --------- + ---------- - -- + ---
    2*(1 + x)   2*(-1 + x)   6     6
General simplification [src] 
    /      2\ /     2      \
    \-1 + x /*\6 - x  + 7*x/
x + ------------------------
               6            
----------------------------
                2           
          -1 + x
$$\frac{x + \frac{\left(x^{2} - 1\right) \left(- x^{2} + 7 x + 6\right)}{6}}{x^{2} - 1}$$ 
(x + (-1 + x^2)*(6 - x^2 + 7*x)/6)/(-1 + x^2)
Trigonometric part [src] 
     2                
    x    7*x      x   
1 - -- + --- + -------
    6     6          2
               -1 + x
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + \frac{x}{x^{2} - 1} + 1$$ 
1 - x^2/6 + 7*x/6 + x/(-1 + x^2)
Powers [src] 
     2                
    x    7*x      x   
1 - -- + --- + -------
    6     6          2
               -1 + x
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + \frac{x}{x^{2} - 1} + 1$$ 
1 - x^2/6 + 7*x/6 + x/(-1 + x^2)
Assemble expression [src] 
     2                
    x    7*x      x   
1 - -- + --- + -------
    6     6          2
               -1 + x
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + \frac{x}{x^{2} - 1} + 1$$ 
1 - x^2/6 + 7*x/6 + x/(-1 + x^2)
Common denominator [src] 
     2                
    x    7*x      x   
1 - -- + --- + -------
    6     6          2
               -1 + x
$$- \frac{x^{2}}{6} + \frac{7 x}{6} + \frac{x}{x^{2} - 1} + 1$$ 
1 - x^2/6 + 7*x/6 + x/(-1 + x^2)
Combinatorics [src] 
 /         4      2      3\ 
-\6 + x + x  - 7*x  - 7*x / 
----------------------------
     6*(1 + x)*(-1 + x)
$$- \frac{x^{4} - 7 x^{3} - 7 x^{2} + x + 6}{6 \left(x - 1\right) \left(x + 1\right)}$$ 
-(6 + x + x^4 - 7*x^2 - 7*x^3)/(6*(1 + x)*(-1 + x))
Numerical answer [src] 
1.0 + 1.16666666666667*x - 0.166666666666667*x^2 + x/(-1.0 + x^2)
1.0 + 1.16666666666667*x - 0.166666666666667*x^2 + x/(-1.0 + x^2)
Rational denominator [src] 
      /      2\ /     2      \
6*x + \-1 + x /*\6 - x  + 7*x/
------------------------------
                  2           
          -6 + 6*x
$$\frac{6 x + \left(x^{2} - 1\right) \left(- x^{2} + 7 x + 6\right)}{6 x^{2} - 6}$$ 
(6*x + (-1 + x^2)*(6 - x^2 + 7*x))/(-6 + 6*x^2)
Combining rational expressions [src] 
      /      2\ /     2      \
6*x + \-1 + x /*\6 - x  + 7*x/
------------------------------
           /      2\          
         6*\-1 + x /
$$\frac{6 x + \left(x^{2} - 1\right) \left(- x^{2} + 7 x + 6\right)}{6 \left(x^{2} - 1\right)}$$ 
(6*x + (-1 + x^2)*(6 - x^2 + 7*x))/(6*(-1 + x^2))
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