Prove that, for real values of \(x\), the function \[\frac{2x+1}{x^2-1}\] can take all real values. Sketch the graph of the function, and prove that it has a point of inflection between \(x=-1\) and \(x=+1\).

Prove that, for real values of \(x\), the function \[\frac{2x+1}{x^2-1}\] can take all real values. Sketch the graph of the function, and prove that it has a point of inflection between \(x=-1\) and \(x=+1\).