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a hole is where the bottom gets canceled out by a like facotr on the top, so factor your top as well

(x-5)(x-4)
---------
2x(x-4)

horizontal asymp are the most fun

there is a hole at x=4; and a VA at x = 0

are you sure that the horizontal asymptote is 1/2 because i thought it was 2

its 1/2

you take the limit as x goes to infinity

divide top and bottom by x^2 to clear things up and yeah, you end up with 1/2

ok and what is the slant?

the slant is when you do long division. so what is the slant?

its a line as that the curve gets closer to as x gets closer to infinity

there.....is.....NO .....slant.......to .....your.....problem.....