Since you said he's cruel, he might be being extremely tricky because a tangent line cannot be both horizontal and vertical, but I'll assume he isn't quite that bad, anyway

you would do exactly what you thought... solve for when the denominator is 0 and the numerator is 0, but depending on how "cruel" he is, your answer for the denominator=0 will be x=1, which doesnt correspond to a point on the curve as it creates a vertical assymptote