SOLUTION: This is a rational inequality problem, I need help with. a/a+2

SOLUTION: This is a rational inequality problem, I need help with. a/a+2 > 0, any suggestions, please.

Question 27749: This is a rational inequality problem, I need help with.
a/a+2 > 0, any suggestions, please.
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
this has asymptotes, so there is a break in the curve.

Possibly the best approach is to sketch it, so you can see when it is greater than zero.

We need to figure out the asymptotes. Looking at the equation, if a=-2, the denominator would then be zero and hence the equation is infinite, so a=-2 is NOT allowed: it is the vertical asymptote.

How, for the horizontal one, consider huge values of a, say 1000...we get 1000/1002 which is nearly 1. Pick 100000, we get 100000/100002...even closer to 1, so "y"=1 is the horizontal asymptote.

Now, where does the curve cross the axes?

when y=0, a = 0, so we can then draw in the 2 parts of the curve...i cannot do it here, so you will have to do it.

From that you can see that the curve is >0 when a>0 and also a<-2.

jon.

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