Precalculus Examples

g (a) = 3 a + 2

$g (a) = 3 a + 2$

f (a) = 2 a - 4

$f (a) = 2 a - 4$ Find

(\frac{g}{f}) (3)

$(\frac{g}{f}) (3)$

Step 1

Evaluate

\frac{g}{f}

$\frac{g}{f}$ .

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Step 1.1

Replace the function designators in

\frac{g}{f}

$\frac{g}{f}$ with the actual functions.

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

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

Step 1.2

Factor

2

$2$ out of

2 a - 4

$2 a - 4$ .

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Step 1.2.1

Factor

2

$2$ out of

2 a

$2 a$ .

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

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

Step 1.2.2

Factor

2

$2$ out of

- 4

$- 4$ .

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

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

Step 1.2.3

Factor

2

$2$ out of

2 a + 2 \cdot - 2

$2 a + 2 \cdot - 2$ .

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

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

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

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

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

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

Step 2

Evaluate

\frac{g}{f}

$\frac{g}{f}$ at

3

$3$ .

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

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

Step 3

Simplify

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

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

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Step 3.1

Remove parentheses.

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

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

Step 3.2

Simplify the numerator.

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Step 3.2.1

Multiply

3

$3$ by

3

$3$ .

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

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

Step 3.2.2

Add

9

$9$ and

2

$2$ .

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

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

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

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

Step 3.3

Simplify the expression.

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Step 3.3.1

Subtract

2

$2$ from

3

$3$ .

\frac{11}{2 \cdot 1}

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

Step 3.3.2

Multiply

2

$2$ by

1

$1$ .

\frac{11}{2}

$\frac{11}{2}$

\frac{11}{2}

$\frac{11}{2}$

\frac{11}{2}

$\frac{11}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{11}{2}

$\frac{11}{2}$

Decimal Form:

5.5

$5.5$

Mixed Number Form:

5 \frac{1}{2}

$5 \frac{1}{2}$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$