# Inequality question (when fraction < zero)

1. Jan 19, 2010

### page13

1. The problem statement, all variables and given/known data

Solve for t:

[-2(t2+1) / 9(t2-1)] < 0

3. The attempt at a solution

I know that the answer is -inf<t<-1 and 1<t<inf, but how do I show the calculation to get that answer? When I tried, I narrowed it down to t<root-1, but that's not possible (without complex numbers) and doesn't match the answer???

2. Jan 19, 2010

### LCKurtz

Try factoring the denominator and analyzing the signs of the factors.

3. Jan 19, 2010

### page13

So 9(t-1)(t+1), but what do I deduce from that?

4. Jan 19, 2010

### LCKurtz

The sign of a fraction is determined by the signs of its factors. You have a - in front of the fraction and the t2 + 1is always positive. The only places where the denominator changes signs are at 1 and -1. So figure out the signs everywhere else. Wherever you have an even number of negative signs your fraction is negative and an odd number makes it positive.

5. Jan 19, 2010

### page13

Ah OK. So it's more by inspection. I would factor as we have done, and then I'd choose for example -2, 0 and 2 and determine the sign giving me the interval values around 1 and -1, correct?

6. Jan 19, 2010

### LCKurtz

That's the idea. Since those factors can only change sign at their roots, if you check the values at a point on each subinterval you will know the signs on the intervals.

7. Jan 19, 2010

### page13

Awesome. Thanks. Now I can sketch this parametric.