Question

How do you find vertical, horizontal and oblique asymptotes for `(x^2 - 5x + 6)/ (x - 3)`?

Answer 1

Remember: You cannot have three asymptotes at the same time. If the Horizontal Asymptote exists, the Oblique Asymptote doesn't exist. Also, `color (red) (H.A)` `color (red) (follow)` `color (red) (three)` `color (red) (procedures).` Let's say `color (red)n` = highest degree of the numerator and `color (blue)m` = highest degree of the denominator,`color (violet) (if)`:
`color (red)n color (green)< color (blue) m`, `color (red) (H.A => y = 0)`
`color (red)n color (green)= color (blue) m`, `color (red) (H.A => y = a/b)`
`color (red)n color (green)> color (blue) m`, `color (red) (H.A)` `color (red) (doesn't)` `color (red) (EE)`

Here, `(x^2 - 5x + 6)/(x-3)`

`V.A: x-3=0 => x = 3`
`O.A: y=x-2`

Please, take a look at the picture.

The oblique/slant asymptote is found by dividing the numerator by the denominator (long division.)

Notice that I did not do the long division in the way some people excepted me to. I always use the "French" way because I've never understood the English way, also I'm a francophone :) but it is the same answer.

Hope this helps :)