Find the Domain (x-4)/(x+2)+2/(x-2)=17/(x^2-4)

$\frac{x - 4}{x + 2} + \frac{2}{x - 2} = \frac{17}{x^{2} - 4}$

Step 1

Set the denominator in $\frac{x - 4}{x + 2}$ 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 $\frac{2}{x - 2}$ equal to $0$ to find where the expression is undefined.

$x - 2 = 0$

Step 4

Add $2$ to both sides of the equation.

$x = 2$

Step 5

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

Interval Notation:

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

Set-Builder Notation:

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

Step 6