lim t-> -infinity for sqrt(4t^2-5t-1)/(2t-3)

Question

I get infinity or -infinity, but the real answer is -1. How does this occur?

Answer 1

as x gets large, higher powers dominate, so

√(4t^2-5t-1) -> √(4t^2) = |2t|
(2t-3) -> 2t

make sense?