Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewSo, what we need to do is first get a zero on one side of the inequality so we can usethe above information. For this problem that has already been done. Now, determinewhere the numerator is zero (since the whole expression will be zero there) and wherethe denominator is zero (since we will get division by zero there).At this point the process is identical to polynomial inequalities with one exceptionwhen we go to write down the answer. The points found above will divide thenumber line into regions in which the inequality will either always be true or alwaysbe false. So, pick test points from each region, test them in the inequality and get thesolution from the results.For this problem the numerator will be zero at x = 3 and the denominator will be zeroat x = − 2. The number line, along with the tests is shown below.So, from this number line it looks like the two outer regions will satisfy theinequality. We need to be careful with the endpoints however. We will include x = 3because this will make the rational expression zero and so will be part of the solution.On the other hand, x = − 2 will give division by zero and so MUST be excluded fromthe solution since division by zero is never allowed.The solution to this inequality is −∞ < x < − 2 and 3 ≤ x