1) $\left({1+\dfrac{\sqrt a-1}{a-\sqrt a}}\right):\left({\dfrac{a+\sqrt a}{a-1}}+\dfrac{\sqrt a}{a-\sqrt a}\right)$
$=\left[{1+\dfrac{\sqrt a-1}{\sqrt a(\sqrt a-1)}}\right]:\left[{\dfrac{\sqrt a(\sqrt a+1)}{(\sqrt a-1)(\sqrt a+1)}}+\dfrac{\sqrt a}{\sqrt a(\sqrt a-1)}\right]$
$=\left({1+\dfrac{1}{\sqrt a}}\right):\left({\dfrac{\sqrt a}{\sqrt a-1}}+\dfrac{1}{\sqrt a-1}\right)$
$=\dfrac{\sqrt a+1}{\sqrt a}:\dfrac{\sqrt a+1}{\sqrt a-1}$
$=\dfrac{\sqrt a+1}{\sqrt a}.\dfrac{\sqrt a-1}{\sqrt a+1}$
$=\dfrac{\sqrt a-1}{\sqrt a}$
$=1-\dfrac{1}{\sqrt a}$
