Simplify ((x-y)/(a+b))÷((x^2-y^2)/(a^2-b^2))

$\frac{x - y}{a + b} \div \frac{x^{2} - y^{2}}{a^{2} - b^{2}}$

To divide by a fraction, multiply by its reciprocal.

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

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

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

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 $b = y$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x - y$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a + b$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{a - b}{x + y}$