Pre-Algebra Examples

$(3 x - 1) \div (9 x^{2} - 1)$

Step 1

Rewrite the division as a fraction.

$\frac{3 x - 1}{9 x^{2} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$\frac{3 x - 1}{{(3 x)}^{2} - 1}$

Step 2.2

Rewrite $1$ as $1^{2}$ .

$\frac{3 x - 1}{{(3 x)}^{2} - 1^{2}}$

Step 2.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 1$ .

$\frac{3 x - 1}{(3 x + 1) (3 x - 1)}$

Step 3

Cancel the common factor of $3 x - 1$ .

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Step 3.1

Cancel the common factor.

$\frac{3 x - 1}{(3 x + 1) (3 x - 1)}$

Step 3.2

Rewrite the expression.

$\frac{1}{3 x + 1}$