Find vertical tangent lines of $\displaystyle y=(2x-6)/(sqrt x^2+3)$. (how do you do square root symbols?)
$\displaystyle y'=[(12-12x)/(2sqrtx^2+)]/(x^2+3)$
$\displaystyle (x^2+3)=0$
$\displaystyle x=+or- (-sqrt3)$, x=complex number, so there are no vertical tangent lines?
Edit: Or actually, $\displaystyle (x^2+3)$ will never be zero, so the denominator would have to be a root function or a fraction to be a vertical tangent line?