I am used to employing Maple in teaching Calculus. Today, I asked a student to think of finding the vertical asymptote(s) of a function for example, $y=\frac{x+1}{x^2-25}$ by Maple. I wanted her to work with the denominator in someway, but she solve the equation respect to $x$ and then apply the definition of horizontal asymptote for $y^{-1}$.
It looked interesting, but may I ask if this way is legal in calculus for finding vertical asymptote of a function? I want to be sure of this way. Of course, I think there are some certain conditions for a function in this question, like existing $y^{-1}$. Thanks for your any ides.