a) M = $\frac{x^2-2x\sqrt{2}+2}{x^2-2}$
= $\frac{x^2-2x\sqrt{2}+\sqrt{2}^2}{(x-\sqrt{2})(x+\sqrt{2})}$
= $\frac{(x-\sqrt{2})^2}{(x-\sqrt{2})(x+\sqrt{2})}$
= $\frac{x-\sqrt{2}}{(x+\sqrt{2})}$
b) N = $\frac{x+\sqrt{5}}{x^2+2x\sqrt{5}+5}$
= $\frac{x+\sqrt{5}}{x^2+2x\sqrt{5}+\sqrt{5}^2}$
= $\frac{1}{(x+\sqrt{5})}$