Question

What are the asymptotes of (x^2+4)/(6x-5x^2)?

Answer 1

Vertical asymptotes are `x=0,x=6/5` and the horizontal asymptote is `y=-1/5`

Explanation:

writing your term in the form

`(x^2+4)/(x(6-5x))` so we get the Asymptote when the denominator is equal to Zero:

This is `x=0` or `x=6/5`
no we compute the Limit for `x` tends to `infty`

writing

`(x^2(1+4/x^2))/(x^2(6/x-5))` and this tends to `-1/5` for `x` tends to infinity.