Find the Domain (5m^2+m)/(7m)

$\frac{5 m^{2} + m}{7 m}$

Step 1

Set the denominator in $\frac{5 m^{2} + m}{7 m}$ equal to $0$ to find where the expression is undefined.

$7 m = 0$

Step 2

Divide each term in $7 m = 0$ by $7$ and simplify.

Divide each term in $7 m = 0$ by $7$ .

$\frac{7 m}{7} = \frac{0}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 m}{7} = \frac{0}{7}$

Divide $m$ by $1$ .

$m = \frac{0}{7}$

Simplify the right side.

Divide $0$ by $7$ .

$m = 0$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${m | m \neq 0}$

Step 4