Algebra Examples

$\frac{x^{2} - 16}{6 x + 24}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{x^{2} - 4^{2}}{6 x + 24}$

Step 1.2

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 $b = 4$ .

$\frac{(x + 4) (x - 4)}{6 x + 24}$

Step 2

Factor $6$ out of $6 x + 24$ .

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Step 2.1

Factor $6$ out of $6 x$ .

$\frac{(x + 4) (x - 4)}{6 (x) + 24}$

Step 2.2

Factor $6$ out of $24$ .

$\frac{(x + 4) (x - 4)}{6 x + 6 \cdot 4}$

Step 2.3

Factor $6$ out of $6 x + 6 \cdot 4$ .

$\frac{(x + 4) (x - 4)}{6 (x + 4)}$

Step 3

Cancel the common factor of $x + 4$ .

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Step 3.1

Cancel the common factor.

$\frac{(x + 4) (x - 4)}{6 (x + 4)}$

Step 3.2

Rewrite the expression.

$\frac{x - 4}{6}$

Step 4

Split the fraction $\frac{x - 4}{6}$ into two fractions.

$\frac{x}{6} + \frac{- 4}{6}$

Step 5

Cancel the common factor of $- 4$ and $6$ .

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Step 5.1

Factor $2$ out of $- 4$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $6$ .

$\frac{x}{6} + \frac{2 \cdot - 2}{2 \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{x}{6} + \frac{2 \cdot - 2}{2 \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{x}{6} + \frac{- 2}{3}$

Step 6

Move the negative in front of the fraction.

$\frac{x}{6} - \frac{2}{3}$