Pre-Algebra Examples

$\frac{9 x^{2} - 4}{6 x - 4}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{{(3 x)}^{2} - 4}{6 x - 4}$

Step 1.2

Rewrite $4$ as $2^{2}$ .

$\frac{{(3 x)}^{2} - 2^{2}}{6 x - 4}$

Step 1.3

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 $b = 2$ .

$\frac{(3 x + 2) (3 x - 2)}{6 x - 4}$

Step 2

Factor $2$ out of $6 x - 4$ .

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Step 2.1

Factor $2$ out of $6 x$ .

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

Step 2.2

Factor $2$ out of $- 4$ .

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

Step 2.3

Factor $2$ out of $2 (3 x) + 2 (- 2)$ .

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

Step 3

Cancel the common factor of $3 x - 2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{3 x + 2}{2}$

Step 4

Split the fraction $\frac{3 x + 2}{2}$ into two fractions.

$\frac{3 x}{2} + \frac{2}{2}$

Step 5

Divide $2$ by $2$ .

$\frac{3 x}{2} + 1$