Answer to Question #2887 in Differential Equations for jenny

Question

Is x = 3 an asymptote of the function f(x)= (x[sup]2[/sup] -5x+6)/(x-3)? Why?

Answer 1

f(x) = (x² - 5x + 6)/(x-3)
Let's factorize the numerator:
x² - 5x + 6 = (x-3)(x-2)
Thus f(x) = (x-3)(x-2)/(x-3) = x-2.
Therefore x=3 is not the asymptote.