Precalculus Examples

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

Step 1

Set the denominator in $\frac{2}{3 x - 1}$ equal to $0$ to find where the expression is undefined.

$3 x - 1 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $1$ to both sides of the equation.

$3 x = 1$

Step 2.2

Divide each term in $3 x = 1$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x = 1$ by $3$ .

$\frac{3 x}{3} = \frac{1}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{1}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{3}$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, \frac{1}{3}) \cup (\frac{1}{3}, \infty)$

Set-Builder Notation:

${x | x \neq \frac{1}{3}}$

Step 4