Algebra Examples

$\frac{\frac{x + 4}{2}}{\frac{x^{2} - 16}{3}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{x + 4}{2} \cdot \frac{3}{x^{2} - 16}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{x + 4}{2} \cdot \frac{3}{x^{2} - 4^{2}}$

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 $a = x$ and $b = 4$ .

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x + 4$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$\frac{1}{2} \cdot \frac{3}{x - 4}$

Step 3.2

Multiply $\frac{1}{2}$ by $\frac{3}{x - 4}$ .

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