Simplify (y/(x^2-y^2))÷((y^2)/(x-y))

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify terms.

Cancel the common factor of $y$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{x^{2} - y^{2}}$ by $\frac{x - y}{y}$ .

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

Step 3

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 $b = y$ .

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

Step 4

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x - y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Reorder factors in $\frac{1}{(x + y) y}$ .

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