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Expression simplification/ Least common denominator/ y/x-(x*y-x^2)/(y-1)*(y-1)/x^2

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

An expression to simplify:

The solution

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