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

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

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 $b = y$ .

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

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x - y$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $x + y$ by $1$ .

$x + y$