Precalculus Examples

$f (x) = 3 x - 1$ $g (x) = x^{2} - x$ 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.

$\frac{3 x - 1}{x^{2} - x}$

Step 1.2

Factor $x$ out of $x^{2} - x$ .

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Step 1.2.1

Factor $x$ out of $x^{2}$ .

$\frac{3 x - 1}{x \cdot x - x}$

Step 1.2.2

Factor $x$ out of $- x$ .

$\frac{3 x - 1}{x \cdot x + x \cdot - 1}$

Step 1.2.3

Factor $x$ out of $x \cdot x + x \cdot - 1$ .

$\frac{3 x - 1}{x (x - 1)}$

Step 2

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

$\frac{3 (x) - 1}{(x) ((x) - 1)}$

Step 3

Simplify $\frac{3 (x) - 1}{(x) ((x) - 1)}$ .

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Step 3.1

Remove parentheses.

$\frac{3 (x) - 1}{(x) ((x) - 1)}$

Step 3.2

Remove parentheses.

$\frac{3 x - 1}{x (x - 1)}$