Finite Math Examples

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

Step 1

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

$4 x + 3 = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Subtract $3$ from both sides of the equation.

$4 x = - 3$

Step 2.2

Divide each term in $4 x = - 3$ by $4$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $4 x = - 3$ by $4$ .

$\frac{4 x}{4} = \frac{- 3}{4}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 3}{4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{4}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{3}{4}$

Step 3

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

Interval Notation:

$(- \infty, - \frac{3}{4}) \cup (- \frac{3}{4}, \infty)$

Set-Builder Notation:

${x | x \neq - \frac{3}{4}}$

Step 4