Good god! Who thought that the following problem would be a good idea to impose on high school students? This is a real question. This is not in an advanced placement class. This is not a bonus question. This is something that all students taking this class, have to know how to solve.
I'm a computer engineer. I've never ever had to solve an equation like this one. Never. Ever.
"It is pitch black. You are likely to be eaten by a rational inequality."
Am I in favor of teaching math? Hell yes.
Am I in favor of having students learn things they are never going to use in real life? Yes, but only conditionally.
I cannot recall the last time I had to find the zeros of an algebraic function, in real life. However, there's some value in learning to pick among different strategies when factoring quadratic equations.
Still, fair enough. If you want to teach factorization strategies, have at it.
But the problem below? Are you kidding me? There are two solutions I know to this problem. One will take you to the forest of madness. The other one requires you to find the zeros of the nominator and the denominator, and then it is brute force. What elegance is there in brute force? At this point, the students already know how to find the zeroes. The only thing this problem adds is how to brute force your way out of a problem. Yay!
