Basic Math Examples

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

Step 1

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 $b = q$ .

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

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{(p + q) (p - q)}{p + q}$ by cancelling the common factors.

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Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Rewrite the expression.

$\frac{p - q}{1} \div \frac{p + q}{p - q}$

Step 2.2

Divide $p - q$ by $1$ .

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