Question

Find the oblique asymptote of f(x)= x^2+3x-4 / x+4

Answer 1

Have you tried long division?

Answer 2

I'm really clueless sorry >.<

Answer 3

The oblique asymptote is the quotient (result) you get from long division without the remainder.

As it turns out, the numerator is perfectly factorizable: \(x^2+3x-4=(x+4)(x-1)\), so
\[\frac{x^2+3x-4}{x+4}=\frac{(x+4)(x-1)}{x+4}=x-1~~~~\text{ (when }x\not=-4)\]
So the oblique "asymptote" is the line \(x-1\).