Find the domain of x+8/x^2-4

Answer 1

The expression x+8/x^2-4 involves division, so we need to ensure that the denominator is not equal to zero.

First, let's find the values that make the denominator equal to zero. The denominator is x^2-4, so we set it equal to zero and solve for x:

x^2 - 4 = 0.

This equation can be factored into (x-2)(x+2) = 0.

Setting each factor equal to zero, we get:
x-2 = 0, x = 2
x+2 = 0, x = -2

So, the values x = 2 and x = -2 make the denominator equal to zero. Therefore, they are not in the domain of the expression x+8/x^2-4.

The domain is all real numbers except for x = 2 and x = -2. In interval notation, the domain is (-∞, -2) ∪ (-2, 2) ∪ (2, ∞).