How do I find the oblique asymptote of this: y= (x-1)^3 / x^2

Question

I tried to use long division but I don’t get how to do it since x² is not a binomial. I’m also confused about how to divide if the numerator is in brackets and has an exponent. I tried to expand it but it’s still wrong.

Answer 1

divide x² into x³ - 3x² +3x -1 and get y = x-3 + (3x-1)/x²

The remainder term goes to 0 as x goes to +/- infinity, and you find the oblique asymptote as the line left over.

Answer 2

y=x-3 is the oblique asymptote

y = (x-1)^3 = (x^2-2x+1)(x-1) = x^3-3x^2+3x-1

y/x^2 = (x^3-3x^2+3x-1)/x^2 = x -3 + a remainder

y=x-3 is the asymptote