Procedure
A rational inequality is an inequality that contains a rational expression.
Step 1. Write the inequality as one quotient on the left and zero on the right.
[tex]\frac{x-3}{x+2}\le0[/tex]
Step 2. Determine the critical points—the points where the rational expression will be zero or undefined.
The rational expression will be zero when the numerator is zero. x = 3
The rational expression will be undefined when the denominator is zero. x = .2
The critical points are -2 and 3
Step 3. Use the critical points to divide the number line into intervals.
[tex](-\infty,-2),(-2,3\rbrack,\lbrack3,\infty)[/tex]
Step 4. Test a value in each interval.
To find the sign of each factor in an interval, we choose any point in that interval and use it as a test point.
Solution
[tex]\begin{gathered} -2
