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

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

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

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

Step 2

Simplify terms.

Factor $x$ out of $x^{2} + x y$ .

Factor $x$ out of $x^{2}$ .

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

Factor $x$ out of $x y$ .

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

Factor $x$ out of $x \cdot x + x (y)$ .

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

Cancel the common factor of $x + y$ .

Factor $x + y$ out of $x (x + y)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - y}{x - y} \cdot \frac{2 x y}{x}$

Multiply $\frac{x - y}{x - y}$ by $\frac{2 x y}{x}$ .

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

Cancel the common factor of $x - y$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 x y}{x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{2 x y}{x}$

Divide $2 y$ by $1$ .

$2 y$