Linear Algebra Examples

$\frac{3}{x} + \frac{6}{x - 2} = \frac{12}{x^{2} - 2 x}$

Step 1

Set the denominator in $\frac{3}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

Set the denominator in $\frac{6}{x - 2}$ equal to $0$ to find where the expression is undefined.

$x - 2 = 0$

Step 3

Add $2$ to both sides of the equation.

$x = 2$

Step 4

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

Interval Notation:

$(- \infty, 0) \cup (0, 2) \cup (2, \infty)$

Set-Builder Notation:

${x | x \neq 0, 2}$

Step 5