Math Is Fun Forum

Set what lies inside the radicand ≥ 0.

(x - 1)/(x + 2) ≥ 0

Set top and bottom to = 0 and solve for x.

x - 1 = 0

x = 1

x + 2 = 0

x = -2

We now make a number line and test a number from each interval.

<------(-2)-------------(1)-------->

Before we test a number from each interval, we plug x = -2 and x = 1 into (x - 1)/(x + 2) ≥ 0
and check for a true inequality statement.

For x = -2, division by zero is made. So, there is a HOLE at x = -2.

For x = 1, I got 0 ≥ 0 which is a true statement.

To the left of x = -2, I selected -3 for x.
For x = -3, I got 4 ≥ 0.........another true statement.

I then selected a number between -2 and 1.  I selected x = 0.
For x = 0, I got -1/2 ≥ 0 which is a false statement.

Lastly, I selected a number to the right of x = 1 and that number is 2.
For x = 2, I got 1/4 ≥ 0 which is a true statement.

By the way, I actually worked out the SUBSTITUTION of all the selected numbers on paper to avoid too much typing.

DOMAIN = (-∞,-2) U [1, ∞)

Did you follow?