Simplify ((a^2-b^2)/(ab))/((a-b)/b)

$\frac{\frac{a^{2} - b^{2}}{a b}}{\frac{a - b}{b}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{a^{2} - b^{2}}{a b} \cdot \frac{b}{a - b}$

Step 2

Simplify terms.

Cancel the common factor of $b$ .

Factor $b$ out of $a b$ .

$\frac{a^{2} - b^{2}}{b a} \cdot \frac{b}{a - b}$

Cancel the common factor.

$\frac{a^{2} - b^{2}}{b a} \cdot \frac{b}{a - b}$

Rewrite the expression.

$\frac{a^{2} - b^{2}}{a} \cdot \frac{1}{a - b}$

Multiply $\frac{a^{2} - b^{2}}{a}$ by $\frac{1}{a - b}$ .

$\frac{a^{2} - b^{2}}{a (a - b)}$

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 $b = b$ .

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

Step 4

Cancel the common factor of $a - b$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{a + b}{a}$