Evaluting the limit $\lim_{x\rightarrow\infty}\frac{1}{\sqrt{x^{2}-4x+1}-x+2}$ I'm attempting to evaluate the limit
$\lim_{x\rightarrow\infty}\frac{1}{\sqrt{x^{2}-4x+1}-x+2}$
I got it reduced to the following
$\lim_{x\rightarrow\infty}\frac{\sqrt{\frac{1}{\left(x-2\right)^{2}}-\frac{3}{\left(x-2\right)^{4}}}+1}{1-\frac{3}{\left(x-2\right)^{2}}-1}$
But putting in $\infty$ I get $\frac{1}{0}$ and, what's worse, Mathematica tells me the limit is equal to $-\infty$. Where am I going wrong?

Hint: multiply top and bottom by $\sqrt{x^2-4x+1}+x-2$.
Additional hint upon request: $\lim_{x\rightarrow \infty}\sqrt{x^2-4x+1}=\infty$ and $\lim_{x\rightarrow \infty} x-2=\infty$.
