Inequality question (when fraction < zero)

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Homework Statement



Solve for t:

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

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???
 

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  • #2
LCKurtz
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Try factoring the denominator and analyzing the signs of the factors.
 
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So 9(t-1)(t+1), but what do I deduce from that?
 
  • #4
LCKurtz
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So 9(t-1)(t+1), but what do I deduce from that?


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
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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
LCKurtz
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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
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Awesome. Thanks. Now I can sketch this parametric.
 

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