SOLUTION: Fins the solution set of the inequality 1/(x - 2) < 1/(x + 3)?

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Question 1172392: Fins the solution set of the inequality 1/(x - 2) < 1/(x + 3)?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x+-+2%29+%3C+1%2F%28x+%2B+3%29

1%2F%28x+-+2%29+-+1%2F%28x+%2B+3%29+%3C+0

%28%28x+%2B+3%29-%28x+-+2%29%29%2F%28%28x+-+2%29%28x+%2B+3%29%29%3C0

%28x+%2B+3-x+%2B+2%29%2F%28%28x+-+2%29%28x+%2B+3%29%29%3C0

%285%29%2F%28%28x+-+2%29%28x+%2B+3%29%29%3C0

Since the numerator is positive, the denominator must be negative.

%28x+-+2%29%28x+%2B+3%29%3C0

The critical numbers and 2 and -3

test region   test value    (+ or -)?    < 0?  
 x < -3           -4            +          no
-3 < x < 2         0            -         yes
   x > 2           3            +          no

So the solution is -3 < x < 2 

Interval notation (-3, 2)

Edwin