SOLUTION: solve the inequality and express the solution set in interval notation. 6/(x+4) > 6/(x-1)

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Question 728270: solve the inequality and express the solution set in interval notation.
6/(x+4) > 6/(x-1)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
6%2F%28x%2B4%29+%3E+6%2F%28x-1%29, divide both sides by 6,
1%2F%28x%2B4%29%3E1%2F%28x-1%29
1%2F%28x%2B4%29-1%2F%28x-1%29%3E0
%28%28x-1%29-%28x%2B4%29%29%2F%28%28x%2B4%29%28x-1%29%29%3E0
%28-5%29%2F%28%28x%2B4%29%28x-1%29%29%3E0

One of the binomials of the denominator must be positive while the other is negative. The critical points to test separating the intervals are at x=-4 and x=1. Pick any value for x in each of these three intervals and test:

(-infinity, -4)
(-4, +1)
(+1, infinity)

The numerator is negative. You must choose the intervals which make the entire denominator itself be negative.