Sketch the graph of \[y = \frac{5x}{x^2 -1},\] showing clearly the three asymptotes.
Use your graph to find the number of real roots of the equation \[kx-1 = \frac{5x}{x^2 -1},\] when \(k\) is a positive constant.
Show also that there is a range of negative values of \(k\) for which the equation has only one real root. (The precise range of values of \(k\) is not required.)
