Pre-Algebra Examples

$\frac{{(x + 12)}^{2}}{x - 12} \div \frac{x^{2} - 144}{12 x - 144}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{{(x + 12)}^{2}}{x - 12} \cdot \frac{12 x - 144}{x^{2} - 144}$

Step 2

Factor $12$ out of $12 x - 144$ .

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Step 2.1

Factor $12$ out of $12 x$ .

$\frac{{(x + 12)}^{2}}{x - 12} \cdot \frac{12 (x) - 144}{x^{2} - 144}$

Step 2.2

Factor $12$ out of $- 144$ .

$\frac{{(x + 12)}^{2}}{x - 12} \cdot \frac{12 x + 12 \cdot - 12}{x^{2} - 144}$

Step 2.3

Factor $12$ out of $12 x + 12 \cdot - 12$ .

$\frac{{(x + 12)}^{2}}{x - 12} \cdot \frac{12 (x - 12)}{x^{2} - 144}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $144$ as $12^{2}$ .

$\frac{{(x + 12)}^{2}}{x - 12} \cdot \frac{12 (x - 12)}{x^{2} - 12^{2}}$

Step 3.2

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 $b = 12$ .

$\frac{{(x + 12)}^{2}}{x - 12} \cdot \frac{12 (x - 12)}{(x + 12) (x - 12)}$

Step 4

Cancel the common factor of $x + 12$ .

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Step 4.1

Factor $x + 12$ out of ${(x + 12)}^{2}$ .

$\frac{(x + 12) (x + 12)}{x - 12} \cdot \frac{12 (x - 12)}{(x + 12) (x - 12)}$

Step 4.2

Cancel the common factor.

$\frac{(x + 12) (x + 12)}{x - 12} \cdot \frac{12 (x - 12)}{(x + 12) (x - 12)}$

Step 4.3

Rewrite the expression.

$\frac{x + 12}{x - 12} \cdot \frac{12 (x - 12)}{x - 12}$

Step 5

Cancel the common factor of $x - 12$ .

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Step 5.1

Factor $x - 12$ out of $12 (x - 12)$ .

$\frac{x + 12}{x - 12} \cdot \frac{(x - 12) \cdot 12}{x - 12}$

Step 5.2

Cancel the common factor.

$\frac{x + 12}{x - 12} \cdot \frac{(x - 12) \cdot 12}{x - 12}$

Step 5.3

Rewrite the expression.

$(x + 12) \frac{12}{x - 12}$

Step 6

Multiply $x + 12$ by $\frac{12}{x - 12}$ .

$\frac{(x + 12) \cdot 12}{x - 12}$

Step 7

Move $12$ to the left of $x + 12$ .

$\frac{12 (x + 12)}{x - 12}$