Simplify ((y^2-z^2)/(yz))/((y-z)/z)

$\frac{\frac{y^{2} - z^{2}}{y z}}{\frac{y - z}{z}}$

Multiply the numerator by the reciprocal of the denominator.

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

Simplify terms.

Cancel the common factor of $z$ .

Factor $z$ out of $y z$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

Cancel the common factor of $y - z$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{y + z}{y}$