Precalculus Examples

$f (x) = 16 x + 12$ $g (x) = 4 x + 3$ Find: $(\frac{f}{g}) (x)$

Step 1

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

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Step 1.1

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

$\frac{16 x + 12}{4 x + 3}$

Step 1.2

Factor $4$ out of $16 x + 12$ .

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Step 1.2.1

Factor $4$ out of $16 x$ .

$\frac{4 (4 x) + 12}{4 x + 3}$

Step 1.2.2

Factor $4$ out of $12$ .

$\frac{4 (4 x) + 4 (3)}{4 x + 3}$

Step 1.2.3

Factor $4$ out of $4 (4 x) + 4 (3)$ .

$\frac{4 (4 x + 3)}{4 x + 3}$

Step 1.3

Cancel the common factor of $4 x + 3$ .

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Step 1.3.1

Cancel the common factor.

$\frac{4 (4 x + 3)}{4 x + 3}$

Step 1.3.2

Divide $4$ by $1$ .

$4$

Step 2

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

$4$

Step 3

Remove parentheses.

$4$