Algebra Examples

$f (x) = 6 x - 12$ $g (x) = 5 x + 1$ $h (x) = x^{2} - 4$ $(\frac{h}{f}) (x)$

Step 1

Evaluate $\frac{h}{f}$ .

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Step 1.1

Replace the function designators in $\frac{h}{f}$ with the actual functions.

$\frac{x^{2} - 4}{6 x - 12}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

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

$\frac{x^{2} - 2^{2}}{6 x - 12}$

Step 1.2.2

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 $b = 2$ .

$\frac{(x + 2) (x - 2)}{6 x - 12}$

Step 1.3

Simplify terms.

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Step 1.3.1

Factor $6$ out of $6 x - 12$ .

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Step 1.3.1.1

Factor $6$ out of $6 x$ .

$\frac{(x + 2) (x - 2)}{6 (x) - 12}$

Step 1.3.1.2

Factor $6$ out of $- 12$ .

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

Step 1.3.1.3

Factor $6$ out of $6 x + 6 \cdot - 2$ .

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

Step 1.3.2

Cancel the common factor of $x - 2$ .

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Step 1.3.2.1

Cancel the common factor.

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

Step 1.3.2.2

Rewrite the expression.

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

Step 2

Evaluate $\frac{h}{f}$ at $x$ .

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

Step 3

Simplify $\frac{(x) + 2}{6}$ .

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Step 3.1

Remove parentheses.

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

Step 3.2

Remove parentheses.

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