Precalculus Examples

$\frac{m^{2} - 9}{2 m + 6}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $9$ as $3^{2}$ .

$\frac{m^{2} - 3^{2}}{2 m + 6}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = 3$ .

$\frac{(m + 3) (m - 3)}{2 m + 6}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Factor $2$ out of $2 m + 6$ .

Tap for more steps...

Step 2.1.1

Factor $2$ out of $2 m$ .

$\frac{(m + 3) (m - 3)}{2 (m) + 6}$

Step 2.1.2

Factor $2$ out of $6$ .

$\frac{(m + 3) (m - 3)}{2 m + 2 \cdot 3}$

Step 2.1.3

Factor $2$ out of $2 m + 2 \cdot 3$ .

$\frac{(m + 3) (m - 3)}{2 (m + 3)}$

Step 2.2

Cancel the common factor of $m + 3$ .

Tap for more steps...

Step 2.2.1

Cancel the common factor.

$\frac{(m + 3) (m - 3)}{2 (m + 3)}$

Step 2.2.2

Rewrite the expression.

$\frac{m - 3}{2}$