Simplify (x^2-y^2)/((x-y)^2)*1/(x+y)

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

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 $b = y$ .

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

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - y$ and ${(x - y)}^{2}$ .

Multiply by $1$ .

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

Cancel the common factors.

Factor $x - y$ out of ${(x - y)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x - y}$