Simplify ((5xy)/((x-y)(x-y)))((x-y)/(x+y))

$(\frac{5 x y}{(x - y) (x - y)}) (\frac{x - y}{x + y})$

Simplify the denominator.

Raise $x - y$ to the power of $1$ .

$\frac{5 x y}{{(x - y)}^{1} (x - y)} \cdot \frac{x - y}{x + y}$

Raise $x - y$ to the power of $1$ .

$\frac{5 x y}{{(x - y)}^{1} {(x - y)}^{1}} \cdot \frac{x - y}{x + y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 x y}{{(x - y)}^{1 + 1}} \cdot \frac{x - y}{x + y}$

Add $1$ and $1$ .

$\frac{5 x y}{{(x - y)}^{2}} \cdot \frac{x - y}{x + y}$

Simplify terms.

Cancel the common factor of $x - y$ .

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

$\frac{5 x y}{(x - y) (x - y)} \cdot \frac{x - y}{x + y}$

Cancel the common factor.

$\frac{5 x y}{(x - y) (x - y)} \cdot \frac{x - y}{x + y}$

Rewrite the expression.

$\frac{5 x y}{x - y} \cdot \frac{1}{x + y}$

Multiply $\frac{5 x y}{x - y}$ by $\frac{1}{x + y}$ .

$\frac{5 x y}{(x - y) (x + y)}$