Divide ((p^2-q^2)/(p+q))÷((p-q)/(p+q))

$\frac{p^{2} - q^{2}}{p + q} \div \frac{p - q}{p + q}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{p^{2} - q^{2}}{p + q} \cdot \frac{p + q}{p - q}$

Step 2

Cancel the common factor of $p + q$ .

Cancel the common factor.

$\frac{p^{2} - q^{2}}{p + q} \cdot \frac{p + q}{p - q}$

Rewrite the expression.

$(p^{2} - q^{2}) \frac{1}{p - q}$

Step 3

Multiply $p^{2} - q^{2}$ by $\frac{1}{p - q}$ .

$\frac{p^{2} - q^{2}}{p - q}$

Step 4

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

$\frac{(p + q) (p - q)}{p - q}$

Step 5

Cancel the common factor of $p - q$ .

Cancel the common factor.

$\frac{(p + q) (p - q)}{p - q}$

Divide $p + q$ by $1$ .

$p + q$