Precalculus Examples

$g (a) = 3 a + 2$ $f (a) = 2 a - 4$ Find $(\frac{g}{f}) (3)$

Step 1

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

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Step 1.1

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

$\frac{3 a + 2}{2 a - 4}$

Step 1.2

Factor $2$ out of $2 a - 4$ .

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Step 1.2.1

Factor $2$ out of $2 a$ .

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

Step 1.2.2

Factor $2$ out of $- 4$ .

$\frac{3 a + 2}{2 a + 2 \cdot - 2}$

Step 1.2.3

Factor $2$ out of $2 a + 2 \cdot - 2$ .

$\frac{3 a + 2}{2 (a - 2)}$

Step 2

Evaluate $\frac{g}{f}$ at $3$ .

$\frac{3 (3) + 2}{2 ((3) - 2)}$

Step 3

Simplify $\frac{3 (3) + 2}{2 ((3) - 2)}$ .

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Step 3.1

Remove parentheses.

$\frac{3 (3) + 2}{2 ((3) - 2)}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

Multiply $3$ by $3$ .

$\frac{9 + 2}{2 (3 - 2)}$

Step 3.2.2

Add $9$ and $2$ .

$\frac{11}{2 (3 - 2)}$

Step 3.3

Simplify the expression.

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Step 3.3.1

Subtract $2$ from $3$ .

$\frac{11}{2 \cdot 1}$

Step 3.3.2

Multiply $2$ by $1$ .

$\frac{11}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{2}$

Decimal Form:

$5.5$

Mixed Number Form:

$5 \frac{1}{2}$