Trigonometry Examples

$\frac{- 20 x^{3} - 13 x^{2} - 14 x - 3}{- 4 x - 1}$

Step 1

Set the denominator in $\frac{- 20 x^{3} - 13 x^{2} - 14 x - 3}{- 4 x - 1}$ equal to $0$ to find where the expression is undefined.

$- 4 x - 1 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $1$ to both sides of the equation.

$- 4 x = 1$

Step 2.2

Divide each term in $- 4 x = 1$ by $- 4$ and simplify.

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Step 2.2.1

Divide each term in $- 4 x = 1$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{1}{- 4}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{1}{- 4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{- 4}$

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.

$x = - \frac{1}{4}$

Step 3

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

Interval Notation:

$(- \infty, - \frac{1}{4}) \cup (- \frac{1}{4}, \infty)$

Set-Builder Notation:

${x | x \neq - \frac{1}{4}}$

Step 4