How do you find the slant asymptote of #f(x)=( x^2+x-6)/(x-3)#?

1 Answer
Mar 28, 2018

Answer:

slant asymptote: #y = x + 4#

Explanation:

Because the degree of the numerator is greater than the degree of the denominator, you can use long division to divide the numerator by the denominator to determine the slant asymptote:
#(x^{2} + x - 6) div (x - 3)#

This results in a quotient of...
#x + 4#

...and a remainder of:
#frac{1}{x - 3}#

Ignore the remainder to find the equation of the slant asymptote:
slant asymptote: #y = x + 4#