Pre-Algebra Examples

$\frac{{(x + 7)}^{2}}{x - 7} \div \frac{x^{2} - 49}{7 x - 49}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Factor $7$ out of $7 x - 49$ .

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Step 2.1

Factor $7$ out of $7 x$ .

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

Step 2.2

Factor $7$ out of $- 49$ .

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

Step 2.3

Factor $7$ out of $7 x + 7 \cdot - 7$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

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 $b = 7$ .

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $x + 7$ .

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Step 4.1.1

Factor $x + 7$ out of ${(x + 7)}^{2}$ .

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $x - 7$ .

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Step 4.2.1

Factor $x - 7$ out of $7 (x - 7)$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$(x + 7) \frac{7}{x - 7}$

Step 4.3

Multiply $x + 7$ by $\frac{7}{x - 7}$ .

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

Step 4.4

Move $7$ to the left of $x + 7$ .

$\frac{7 (x + 7)}{x - 7}$