Find the Domain (m^2+2m-24)/(m^2-3m)

$\frac{m^{2} + 2 m - 24}{m^{2} - 3 m}$

Step 1

Set the denominator in $\frac{m^{2} + 2 m - 24}{m^{2} - 3 m}$ equal to $0$ to find where the expression is undefined.

$m^{2} - 3 m = 0$

Step 2

Solve for $m$ .

Factor $m$ out of $m^{2} - 3 m$ .

Factor $m$ out of $m^{2}$ .

$m \cdot m - 3 m = 0$

Factor $m$ out of $- 3 m$ .

$m \cdot m + m \cdot - 3 = 0$

Factor $m$ out of $m \cdot m + m \cdot - 3$ .

$m (m - 3) = 0$

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

$m = 0$

$m - 3 = 0$

Set $m$ equal to $0$ .

$m = 0$

Set $m - 3$ equal to $0$ and solve for $m$ .

Set $m - 3$ equal to $0$ .

$m - 3 = 0$

Add $3$ to both sides of the equation.

$m = 3$

The final solution is all the values that make $m (m - 3) = 0$ true.

$m = 0, 3$

Step 3

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

Interval Notation:

$(- \infty, 0) \cup (0, 3) \cup (3, \infty)$

Set-Builder Notation:

${m | m \neq 0, 3}$

Step 4