Pre-Algebra Examples

$\frac{4 x - 12}{x^{2} - 9}$

Step 1

Factor $4$ out of $4 x - 12$ .

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Step 1.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 12}{x^{2} - 9}$

Step 1.2

Factor $4$ out of $- 12$ .

$\frac{4 x + 4 \cdot - 3}{x^{2} - 9}$

Step 1.3

Factor $4$ out of $4 x + 4 \cdot - 3$ .

$\frac{4 (x - 3)}{x^{2} - 9}$

Step 2

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

$\frac{4 (x - 3)}{x^{2} - 3^{2}}$

Step 3

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

$\frac{4 (x - 3)}{(x + 3) (x - 3)}$

Step 4

Reduce the expression $\frac{4 (x - 3)}{(x + 3) (x - 3)}$ by cancelling the common factors.

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Step 4.1

Cancel the common factor.

$\frac{4 (x - 3)}{(x + 3) (x - 3)}$

Step 4.2

Rewrite the expression.

$\frac{4}{x + 3}$