Algebra Examples

$f (x) = 3 x - 6$ $g (x) = x - 2$

Step 1

Find the quotient of the functions.

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Step 1.1

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

$\frac{3 x - 6}{x - 2}$

Step 1.2

Simplify.

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Step 1.2.1

Factor $3$ out of $3 x - 6$ .

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Step 1.2.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{x - 2}$

Step 1.2.1.2

Factor $3$ out of $- 6$ .

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

Step 1.2.1.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

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

Step 1.2.2

Cancel the common factor of $x - 2$ .

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Step 1.2.2.1

Cancel the common factor.

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

Step 1.2.2.2

Divide $3$ by $1$ .

$3$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3