Algebra Examples

$\frac{x}{7 x - 6}$

Step 1

Set the denominator in $\frac{x}{7 x - 6}$ equal to $0$ to find where the expression is undefined.

$7 x - 6 = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Add $6$ to both sides of the equation.

$7 x = 6$

Step 2.2

Divide each term in $7 x = 6$ by $7$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $7 x = 6$ by $7$ .

$\frac{7 x}{7} = \frac{6}{7}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{6}{7}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{7}$

Step 3

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

Interval Notation:

$(- \infty, \frac{6}{7}) \cup (\frac{6}{7}, \infty)$

Set-Builder Notation:

${x | x \neq \frac{6}{7}}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \frac{1}{7}) \cup (\frac{1}{7}, \infty)$

Set-Builder Notation:

${y | y \neq \frac{1}{7}}$

Step 5

Determine the domain and range.

Domain: $(- \infty, \frac{6}{7}) \cup (\frac{6}{7}, \infty), {x | x \neq \frac{6}{7}}$

Range: $(- \infty, \frac{1}{7}) \cup (\frac{1}{7}, \infty), {y | y \neq \frac{1}{7}}$

Step 6