Find oblique asymptote

Question

(X^2 - 2x - 8)/(x-1)

find the asymptote

Answer 1

To get oblique asymptote we have to perform division: (x² - 2x - 8)/(x - 1) using synthetic division

1| 1 -2 -8

1 -1

1 -1 -9

Because (x² - 2x - 8)/(x - 1) = x - 1 - 9/(x - 1);

Because y = x - 1 is oblique asymptote to the graph of f(x) = (x² - 2x - 8)/(x - 1).

Answer: y = x - 1

Answer 2

To find the oblique asymptote equation, you need to divide. This specific problem can be done by synthetic division. Since that is easier than long division, I will do that.

1 | 1 -2 -8

1 -1

1 -1 -9

The remainder of -9 doesn't matter. The remaining equation is the asymptote equation you are looking for

y=x-1