Linear Algebra Examples

$\frac{2}{x + 2} + \frac{1}{x + 4} = \frac{4}{x^{2} + 6 x + 8}$

Step 1

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

$x + 2 = 0$

Step 2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 3

Set the denominator in $\frac{1}{x + 4}$ equal to $0$ to find where the expression is undefined.

$x + 4 = 0$

Step 4

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 5

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

Interval Notation:

$(- \infty, - 4) \cup (- 4, - 2) \cup (- 2, \infty)$

Set-Builder Notation:

${x | x \neq - 2, - 4}$

Step 6