Hi,

I hope someone can help. I'm trying to understand in what cases it is okay for me to remove the denominator from a rational inequality without having to flip the inequality sign. I thought it was okay in the event that I knew that the denominator was positive. However the following word problem appears to prove otherwise...

$\displaystyle A(t) = \frac{360}{t+6}$

$\displaystyle C(t) = \frac{50}{41-2t}$

I'm trying to determine when A(t) > C(t). Both functions measure population size over "t" years starting at t=0. Since I know that the denominator is positive, this means that I can remove the denominator without having to flip the inequality sign.

I got the solution which was A(t) > C(t) when t < 18.78. However, I know that this is only one of my solutions because when I compare the graphs using graphing technology, I also notice that A(t) > C(t) when t > 20.5. Can someone please explain to me why this solution did not show up as part of my solution set?