Precalculus Examples

$\frac{\frac{2}{x}}{\frac{x}{x - 1}}$

Step 1

Set the denominator in $\frac{2}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

Set the denominator in $\frac{x}{x - 1}$ equal to $0$ to find where the expression is undefined.

$x - 1 = 0$

Step 3

Add $1$ to both sides of the equation.

$x = 1$

Step 4

Set the denominator in $\frac{\frac{2}{x}}{\frac{x}{x - 1}}$ equal to $0$ to find where the expression is undefined.

$\frac{x}{x - 1} = 0$

Step 5

Set the numerator equal to zero.

$x = 0$

Step 6

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

Interval Notation:

$(- \infty, 0) \cup (0, 1) \cup (1, \infty)$

Set-Builder Notation:

${x | x \neq 0, 1}$

Step 7