Find the Domain f(x)=(3x-8)/(4x+20)

$f (x) = \frac{3 x - 8}{4 x + 20}$

Step 1

Set the denominator in $\frac{3 x - 8}{4 x + 20}$ equal to $0$ to find where the expression is undefined.

$4 x + 20 = 0$

Step 2

Solve for $x$ .

Subtract $20$ from both sides of the equation.

$4 x = - 20$

Divide each term in $4 x = - 20$ by $4$ and simplify.

Divide each term in $4 x = - 20$ by $4$ .

$\frac{4 x}{4} = \frac{- 20}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 20}{4}$

Divide $x$ by $1$ .

$x = \frac{- 20}{4}$

Simplify the right side.

Divide $- 20$ by $4$ .

$x = - 5$

Step 3

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

Interval Notation:

$(- \infty, - 5) \cup (- 5, \infty)$

Set-Builder Notation:

${x | x \neq - 5}$

Step 4