# How to find a if the function below doesn't have a vertical asymptotes. f(x)=(x2−ax+2)/(x−2)

Asymptotes of function
How to find a if the function below doesn't have a vertical asymptotes.
$f\left(x\right)=\frac{{x}^{2}-ax+2}{x-2}$
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penangrl
A function like that has vertical asymptote when it's denominator is 0, that happens when x=2
$f\left(x\right)=\frac{{x}^{2}-ax+2}{x-2}$
But since we don't want f(x) to have a vertical asymptotes, then x−2 must be a factor of ${x}^{2}+ax+2$
${x}^{2}-ax+2=\left(x-2\right)\left(x-b\right)$
$6-2a=0$
$f\left(x\right)=\frac{{x}^{2}-3x+2}{x-2}$
$f\left(x\right)=\frac{\left(x-2\right)\cdot \left(x-1\right)}{x-2}$
$f\left(x\right)=\left(x-1\right)$
###### Not exactly what you’re looking for?
Hint: This can only happen if x−2 is a factor of the numerator, so it can "cancel" the x−2 in the denominator. What does $a$ have to be for this to be true?