SOLUTION: how am I to solve an inequality of this type(x+2)(x+2)/(x+1)<0 using cases

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Question 12352: how am I to solve an inequality of this type(x+2)(x+2)/(x+1)<0 using cases
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B2%29%28x%2B2%29%2F%28x%2B1%29%3C0
is +%28x%2B2%29%5E2%2F%28x%2B1%29+%3C+0+
Hence,the numberator and the denominator are of different sign.
But +%28x%2B2%29%5E2+%3E=+0+ for all real x.

The denomiator +x%2B1+ must be negative and the nmerator
x%2B2+ cannot be 0.

So, +%28x%2B2%29%5E2%2F%28x%2B1%29+%3C+0+ implies
+x%2B1%3C0+and+x+is+not+equal+to+-2

We obtain the solution set +-2+%3C+x+%3C+-1+or+x+%3C+-2
In the interval notaion: (-oo,-2) U (-2,-1).
The above is the shortest way to solve this kind of questions.
Try to think about it. [In fact, I can get the answer by direct view
in a second. ]
If you really want to consider cases
Look the sign of the given %28x%2B2%29%5E2%2F%28x%2B1%29 on the intervals
(-oo,-2),(-2,-1), (-1,+oo). You will see.


-----------*-----*----------------------
-oo -2 -1 +oo

Kenny