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

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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

Step 3

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

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

Step 4

Reduce the expression by cancelling the common factors.

Cancel the common factor of $z + y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a - b$ .

Factor $a - b$ out of $(a + b) (a - b)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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