Find all vertical and horizontal asymtote(s) if any, of the following rational equation...

Question

suwhitney · Answer

$$f(x)=\frac{ (6x^2+x+12) }{(3x^2-5x+2)(x^2+2) }$$

I do not know how to get the answer of this question... :/

anonymous · Answer

Vertical asymptotes are a kind of discontinuity that happen where x causes division by zero.

anonymous · Answer

It's possible that a factor in the denominator will cancel with a factor in the numerator, seemingly taking away that discontinuity, but what happens is the discontinuity is a hole in the graph instead of an asymptote.

So, the first step is to factor everything as much as possible, then look for possible division-by-zero.

anonymous · Answer

The x^2+2 on the bottom can't be factored, but try factoring those two quadratic trinomials.