Precalculus Examples

$\frac{5 x}{3 x (x + 12)}$

Step 1

Set the denominator in $\frac{5 x}{3 x (x + 12)}$ equal to $0$ to find where the expression is undefined.

$3 x (x + 12) = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 12 = 0$

Step 2.2

Set $x$ equal to $0$ .

$x = 0$

Step 2.3

Set $x + 12$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.3.1

Set $x + 12$ equal to $0$ .

$x + 12 = 0$

Step 2.3.2

Subtract $12$ from both sides of the equation.

$x = - 12$

Step 2.4

The final solution is all the values that make $3 x (x + 12) = 0$ true.

$x = 0, - 12$

Step 3

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

Interval Notation:

$(- \infty, - 12) \cup (- 12, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0, - 12}$

Step 4