(a) Let \(a, b\) be rationals and \(x\) irrational. Show that if \(\frac{x+a}{x+b}\) is rational, then \(a=b\).

(b) Let \(x, y\) be rationals such that \(\frac{x^{2}+x+\sqrt{2}}{y^{2}+y+\sqrt{2}}\) is also rational. Prove that either \(x=y\) or \(x+y=-1\).