Calculate $lim_{x \to (\frac{9}{8})} \frac{12x}{9-8x}$ and $lim_{x\to(-\frac{9}{8})} \frac{12x}{9-8x}$.
I am confused how to do this. L'hospital, substitution and conjugates will not solve this as they result in the division of zero. I tried factoring out the largest degree:
(x/x)(12/[9/x]-8)
integer over variable results in 0:
12/ (0 - 8) =
12/-8 =
-3/2
However, upon further investigation this is the limit as it approaches infinity. I have tried a few other things, but none have resulted in a correct answer, this is as close as I have gotten. What do I have to do to get $x \to \frac{9}{8}$ instead of $x \to (+)\infty$? Thanks.