SOLUTION: solve : ((x² -2x -3)/(x+1)) ≤ 0

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Question 1167552: solve : ((x² -2x -3)/(x+1)) ≤ 0
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


%28x%5E2-2x-3%29%2F%28x%2B1%29%3C=0

In factored form that is

%28%28x-3%29%28x%2B1%29%29%2F%28x%2B1%29%3C=0

With the like factors of (x+1) in both numerator and denominator, there will be a hole in the graph at x=-1; everywhere else the graph will be the same as the graph of x-3%3C=0

x-3%3C=0
x%3C=3

The original inequality is true whenever x is less than or equal to 3, except that it is undefined at x=-1.

ANSWER: (-infinity, -1) union (-1,3]

Here is a graph of the given function; it won't show the hole in the graph at (-1,-4):
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%28x%5E2-2x-3%29%2F%28x%2B1%29%29

A graphing utility like a TI-83 calculator will show the hole if an appropriate viewing window is used.