Algebra Examples

$y = \frac{5}{6 x - 72}$

Set the denominator in $\frac{5}{6 x - 72}$ equal to $0$ to find where the expression is undefined.

$6 x - 72 = 0$

Solve for $x$ .

Tap for more steps...

Add $72$ to both sides of the equation.

$6 x = 72$

Divide each term in $6 x = 72$ by $6$ and simplify.

Tap for more steps...

Divide each term in $6 x = 72$ by $6$ .

$\frac{6 x}{6} = \frac{72}{6}$

Simplify the left side.

Tap for more steps...

Cancel the common factor of $6$ .

Tap for more steps...

Cancel the common factor.

$\frac{6 x}{6} = \frac{72}{6}$

Divide $x$ by $1$ .

$x = \frac{72}{6}$

Simplify the right side.

Tap for more steps...

Divide $72$ by $6$ .

$x = 12$

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

Interval Notation:

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

Set-Builder Notation:

${x | x \neq 12}$