Precalculus Examples

$\frac{x}{6 x + 25}$

Step 1

Set the denominator in $\frac{x}{6 x + 25}$ equal to $0$ to find where the expression is undefined.

$6 x + 25 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $25$ from both sides of the equation.

$6 x = - 25$

Step 2.2

Divide each term in $6 x = - 25$ by $6$ and simplify.

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Step 2.2.1

Divide each term in $6 x = - 25$ by $6$ .

$\frac{6 x}{6} = \frac{- 25}{6}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $6$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 25}{6}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 25}{6}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{25}{6}$

Step 3

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

Interval Notation:

$(- \infty, - \frac{25}{6}) \cup (- \frac{25}{6}, \infty)$

Set-Builder Notation:

${x | x \neq - \frac{25}{6}}$

Step 4