Question 576496
Do you mean


*[tex \LARGE y = \frac{1}{x} - 1], or


*[tex \LARGE y = \frac{1}{x-1}]?


In either case, quadratics or discriminants won't help. Take dy/dx of both sides:


*[tex \LARGE \frac{dy}{dx} = -x^2], or


*[tex \LARGE \frac{dy}{dx} = -(x-1)^2]


depending on whether you intend (1/x)-1 or 1/(x-1). Set dy/dx = -1, solve for x, find the equation of the tangent line using point-slope form (since you have the slope and you can find a point on the graph).