Basic Math Examples

$\frac{x^{2} - 9}{3 x - 9}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{x^{2} - 3^{2}}{3 x - 9}$

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 $a = x$ and $b = 3$ .

$\frac{(x + 3) (x - 3)}{3 x - 9}$

Step 2

Simplify terms.

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Step 2.1

Factor $3$ out of $3 x - 9$ .

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Step 2.1.1

Factor $3$ out of $3 x$ .

$\frac{(x + 3) (x - 3)}{3 (x) - 9}$

Step 2.1.2

Factor $3$ out of $- 9$ .

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

Step 2.1.3

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

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

Step 2.2

Cancel the common factor of $x - 3$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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