# Answer to Question #2887 in Differential Equations for jenny

Question #2887

Is x = 3 an asymptote of the function f(x)= (x

^{2}-5x+6)/(x-3)? Why?Expert's answer

f(x) = (x

Let's factorize the numerator:

x

Thus f(x) = (x-3)(x-2)/(x-3) = x-2.

Therefore x=3 is not the asymptote.

^{2}- 5x + 6)/(x-3)Let's factorize the numerator:

x

^{2}- 5x + 6 = (x-3)(x-2)Thus f(x) = (x-3)(x-2)/(x-3) = x-2.

Therefore x=3 is not the asymptote.

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