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Expression simplification/ Least common denominator/ ((x/(y-x))^-2)*((x^2+x*y)/(((x+y)^2)-4*x*y))

Least common denominator ((x/(y-x))^-2)*((x^2+x*y)/(((x+y)^2)-4*x*y))

An expression to simplify:

The solution

You have entered [src] 
/     2          \
|    x  + x*y    |
|----------------|
|       2        |
\(x + y)  - 4*x*y/
------------------
            2     
     /  x  \      
     |-----|      
     \y - x/
$$\frac{\left(x^{2} + x y\right) \frac{1}{- 4 x y + \left(x + y\right)^{2}}}{x^{2} \frac{1}{\left(- x + y\right)^{2}}}$$ 
((x^2 + x*y)/((x + y)^2 - 4*x*y))/(x/(y - x))^2
General simplification [src] 
x + y
-----
  x
$$\frac{x + y}{x}$$ 
(x + y)/x
Numerical answer [src] 
(y - x)^2*(x^2 + x*y)/(x^2*((x + y)^2 - 4.0*x*y))
(y - x)^2*(x^2 + x*y)/(x^2*((x + y)^2 - 4.0*x*y))
Assemble expression [src] 
        2 / 2      \ 
 (y - x) *\x  + x*y/ 
---------------------
 2 /       2        \
x *\(x + y)  - 4*x*y/
$$\frac{\left(- x + y\right)^{2} \left(x^{2} + x y\right)}{x^{2} \left(- 4 x y + \left(x + y\right)^{2}\right)}$$ 
(y - x)^2*(x^2 + x*y)/(x^2*((x + y)^2 - 4*x*y))
Expand expression [src] 
        2 / 2      \ 
 (y - x) *\x  + x*y/ 
---------------------
 2 /       2        \
x *\(x + y)  - 4*x*y/
$$\frac{\left(- x + y\right)^{2} \left(x^{2} + x y\right)}{x^{2} \left(- 4 x y + \left(x + y\right)^{2}\right)}$$ 
(y - x)^2*(x^2 + x*y)/(x^2*((x + y)^2 - 4*x*y))
Powers [src] 
        2 / 2      \ 
 (y - x) *\x  + x*y/ 
---------------------
 2 /       2        \
x *\(x + y)  - 4*x*y/
$$\frac{\left(- x + y\right)^{2} \left(x^{2} + x y\right)}{x^{2} \left(- 4 x y + \left(x + y\right)^{2}\right)}$$ 
(y - x)^2*(x^2 + x*y)/(x^2*((x + y)^2 - 4*x*y))
Combining rational expressions [src] 
         2          
  (y - x) *(x + y)  
--------------------
  /       2        \
x*\(x + y)  - 4*x*y/
$$\frac{\left(- x + y\right)^{2} \left(x + y\right)}{x \left(- 4 x y + \left(x + y\right)^{2}\right)}$$ 
(y - x)^2*(x + y)/(x*((x + y)^2 - 4*x*y))
Combinatorics [src] 
x + y
-----
  x
$$\frac{x + y}{x}$$ 
(x + y)/x
Trigonometric part [src] 
        2 / 2      \ 
 (y - x) *\x  + x*y/ 
---------------------
 2 /       2        \
x *\(x + y)  - 4*x*y/
$$\frac{\left(- x + y\right)^{2} \left(x^{2} + x y\right)}{x^{2} \left(- 4 x y + \left(x + y\right)^{2}\right)}$$ 
(y - x)^2*(x^2 + x*y)/(x^2*((x + y)^2 - 4*x*y))
Common denominator [src] 
    y
1 + -
    x
$$1 + \frac{y}{x}$$ 
1 + y/x
Rational denominator [src] 
 2        2              2
x *(x - y)  + x*y*(x - y) 
--------------------------
    2 / 2    2        \   
   x *\x  + y  - 2*x*y/
$$\frac{x^{2} \left(x - y\right)^{2} + x y \left(x - y\right)^{2}}{x^{2} \left(x^{2} - 2 x y + y^{2}\right)}$$ 
(x^2*(x - y)^2 + x*y*(x - y)^2)/(x^2*(x^2 + y^2 - 2*x*y))
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