Basic Math Examples

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

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

Step 1

Set the denominator in

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

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

0

$0$ to find where the expression is undefined.

5 x - 6 = 0

$5 x - 6 = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Add

6

$6$ to both sides of the equation.

5 x = 6

$5 x = 6$

Step 2.2

Divide each term in

5 x = 6

$5 x = 6$ by

5

$5$ and simplify.

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Step 2.2.1

Divide each term in

5 x = 6

$5 x = 6$ by

5

$5$ .

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

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

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of

5

$5$ .

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Step 2.2.2.1.1

Cancel the common factor.

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

Step 2.2.2.1.2

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$