Simplify (x^2-xy-x+y)/(x^2+xy-x-y)

$\frac{x^{2} - x y - x + y}{x^{2} + x y - x - y}$

Step 1

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(x^{2} - x y) - x + y}{x^{2} + x y - x - y}$

Factor out the greatest common factor (GCF) from each group.

$\frac{x (x - 1 y) - (x - y)}{x^{2} + x y - x - y}$

Factor the polynomial by factoring out the greatest common factor, $x - 1 y$ .

$\frac{(x - 1 y) (x - 1)}{x^{2} + x y - x - y}$

Rewrite $- 1 y$ as $- y$ .

$\frac{(x - y) (x - 1)}{x^{2} + x y - x - y}$

Step 2

Simplify the denominator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(x - y) (x - 1)}{(x^{2} + x y) - x - y}$

Factor out the greatest common factor (GCF) from each group.

$\frac{(x - y) (x - 1)}{x (x + y) - (x + y)}$

Factor the polynomial by factoring out the greatest common factor, $x + y$ .

$\frac{(x - y) (x - 1)}{(x + y) (x - 1)}$

Step 3

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{(x - y) (x - 1)}{(x + y) (x - 1)}$

Rewrite the expression.

$\frac{x - y}{x + y}$