Ta có :

$M=\left ( \frac{1}{a-\sqrt{a}}+\frac{1}{\sqrt{a}-1} \right ):\frac{\sqrt{a}+1}{a-2\sqrt{a}+1}$

$M=\left [ \frac{1}{\sqrt{a}(\sqrt{a}-1)}+\frac{1}{\sqrt{a}-1} \right ]:\frac{\sqrt{a}+1}{(\sqrt{a}-1)^{2}}$

$M=\frac{1+\sqrt{a}}{\sqrt{a}(\sqrt{a}-1)}.\frac{(\sqrt{a}-1)^{2}}{\sqrt{a}+1}$

$M=\frac{\sqrt{a}-1}{\sqrt{a}}=1-\frac{1}{\sqrt{a}}$

So sánh M với 1 :

$M=1-\frac{1}{\sqrt{a}}<1$