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Find the Domain (x-1)/(5x-6)

$\frac{x - 1}{5 x - 6}$

Step 1

Set the denominator in

$\frac{x - 1}{5 x - 6}$ equal to

$0$ to find where the expression is undefined.

$5 x - 6 = 0$

Step 2

Solve for

$x$ .

Add

$6$ to both sides of the equation.

$5 x = 6$

Divide each term in

$5 x = 6$ by

$5$ and simplify.

Divide each term in

$5 x = 6$ by

$5$ .

$\frac{5 x}{5} = \frac{6}{5}$

Simplify the left side.

Cancel the common factor of

$5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{6}{5}$

Divide

$x$ by

$1$ .

$x = \frac{6}{5}$

$x = \frac{6}{5}$

$x = \frac{6}{5}$

$x = \frac{6}{5}$

$x = \frac{6}{5}$

Step 3

The domain is all values of

$x$ that make the expression defined.

Interval Notation:

$(- \infty, \frac{6}{5}) \cup (\frac{6}{5}, \infty)$

Set-Builder Notation:

${x | x \neq \frac{6}{5}}$

Step 4

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