Answer
$x=0$
Work Step by Step
We are given the function:
$f(x)=\dfrac{x^2-3x+2}{x^{10}-x^9}$
Compute $\lim\limits_{x \to a} f(x)=\lim\limits_{x \to a} \dfrac{x^2-3x+2}{x^{10}-x^9}=\lim\limits_{x \to a} \dfrac{x^2-x-2x+2}{x^9(x-1)}$
$=\lim\limits_{x \to a} \dfrac{x(x-1)-2(x-1)}{x^9(x-1)}=\lim\limits_{x \to a} \dfrac{(x-1)(x-2)}{x^9(x-1)}$
$=\lim\limits_{x \to a} \dfrac{x-2}{x^9}$
For $a=0$ we have:
$\lim\limits_{x \to 0^-} \dfrac{x-2}{x^9}=\infty$
$\lim\limits_{x \to 0^+} \dfrac{x-2}{x^9}=-\infty$
Therefore $f(x)$ has a vertical asymptote in $x=0$.
