Answer:
y=x+9.
Step-by-step explanation:
the function is [tex]\frac{x^{2}+5x+6}{x-4}[/tex]. Now, the equation of the oblique asymptote is a function y= mx + b where
m = [tex]\lim_{x \to \infty} \frac{f(x)}{x}[/tex]
and b = [tex]\lim_{x \to \infty} f(x)-mx[/tex]
So,
m = [tex]\lim_{x \to \infty} \frac{\frac{x^{2}+5x+6}{x-4}}{x} [/tex]
= [tex]\lim_{x \to \infty} \frac{x^{2}+5x+6}{x^{2}-4x}= 1.[/tex]
and,
b = [tex]\lim_{x \to \infty}\frac{x^{2}+5x+6}{x-4}-x[/tex]
= [tex]\lim_{x \to \infty}\frac{x^{2}+5x+6-x^{2}+4x}{x-4}[/tex]
= [tex]\lim_{x \to \infty}\frac{9x+6}{x-4}= 9.[/tex]
Then, the equation of the oblique asymptote is y= x+9.
