Pre-Algebra Examples

$\frac{36 x^{2} - 49}{2 x - 36} \div \frac{6 x + 7}{x - 6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{36 x^{2} - 49}{2 x - 36} \cdot \frac{x - 6}{6 x + 7}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $36 x^{2}$ as ${(6 x)}^{2}$ .

$\frac{{(6 x)}^{2} - 49}{2 x - 36} \cdot \frac{x - 6}{6 x + 7}$

Step 2.2

Rewrite $49$ as $7^{2}$ .

$\frac{{(6 x)}^{2} - 7^{2}}{2 x - 36} \cdot \frac{x - 6}{6 x + 7}$

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 $a = 6 x$ and $b = 7$ .

$\frac{(6 x + 7) (6 x - 7)}{2 x - 36} \cdot \frac{x - 6}{6 x + 7}$

Step 3

Simplify terms.

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Step 3.1

Factor $2$ out of $2 x - 36$ .

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Step 3.1.1

Factor $2$ out of $2 x$ .

$\frac{(6 x + 7) (6 x - 7)}{2 (x) - 36} \cdot \frac{x - 6}{6 x + 7}$

Step 3.1.2

Factor $2$ out of $- 36$ .

$\frac{(6 x + 7) (6 x - 7)}{2 x + 2 \cdot - 18} \cdot \frac{x - 6}{6 x + 7}$

Step 3.1.3

Factor $2$ out of $2 x + 2 \cdot - 18$ .

$\frac{(6 x + 7) (6 x - 7)}{2 (x - 18)} \cdot \frac{x - 6}{6 x + 7}$

Step 3.2

Cancel the common factor of $6 x + 7$ .

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Step 3.2.1

Cancel the common factor.

$\frac{(6 x + 7) (6 x - 7)}{2 (x - 18)} \cdot \frac{x - 6}{6 x + 7}$

Step 3.2.2

Rewrite the expression.

$\frac{6 x - 7}{2 (x - 18)} (x - 6)$

Step 3.3

Multiply $\frac{6 x - 7}{2 (x - 18)}$ by $x - 6$ .

$\frac{(6 x - 7) (x - 6)}{2 (x - 18)}$