Show that, if \(y=\dfrac{x^2+1}{x^2-a^2},\) \(y\) takes all real values twice, except those for which \(-\dfrac{1}{a^2}\le y\le 1\).

Sketch the curve \(y=\dfrac{x^2+1}{x^2-4}\), indicating its asymptotes.

Show that, if \(y=\dfrac{x^2+1}{x^2-a^2},\) \(y\) takes all real values twice, except those for which \(-\dfrac{1}{a^2}\le y\le 1\).

Sketch the curve \(y=\dfrac{x^2+1}{x^2-4}\), indicating its asymptotes.