Pre-Algebra Examples

$\frac{\frac{1}{k + 2}}{\frac{5}{k^{2} - 4}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{k + 2} \cdot \frac{k^{2} - 4}{5}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{1}{k + 2} \cdot \frac{k^{2} - 2^{2}}{5}$

Step 2.2

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

$\frac{1}{k + 2} \cdot \frac{(k + 2) (k - 2)}{5}$

Step 3

Cancel the common factor of $k + 2$ .

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Step 3.1

Cancel the common factor.

$\frac{1}{k + 2} \cdot \frac{(k + 2) (k - 2)}{5}$

Step 3.2

Rewrite the expression.

$\frac{k - 2}{5}$