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

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

To divide by a fraction, multiply by its reciprocal.

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

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 $b = q$ .

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

Simplify terms.

Cancel the common factor of $p + q$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{p - q}{p + q}$ by $p - q$ .

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

Simplify the numerator.

Raise $p - q$ to the power of $1$ .

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

Raise $p - q$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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