a) $\left(\dfrac{1 - a\sqrt a}{1 - \sqrt a} + \sqrt a\right)\left(\dfrac{1 - \sqrt a}{1 -a}\right)^2$
$= \left(\dfrac{(1 - \sqrt a)(1 + \sqrt a + a)}{1 - \sqrt a} + \sqrt a\right)\left(\dfrac{1 - \sqrt a}{(1 -\sqrt a)(1 + \sqrt a)}\right)^2$
$= (a + 2\sqrt a + 1)\left(\dfrac{1}{1 +\sqrt a}\right)^2$
$= (\sqrt a + 1)\left(\dfrac{1}{1 +\sqrt a}\right)^2 = 1$
b) $\dfrac{a + b}{b^2}\sqrt{\dfrac{a^2b^4}{a^2 + 2ab + b^2}}$
$= \dfrac{a + b}{b^2}\dfrac{|a|b^2}{\sqrt{(a+b)^2}}$
$= (a + b)\dfrac{|a|}{|a + b|}$
$= (a + b)\dfrac{|a|}{a + b}\qquad (a + b > 0)$
$= |a|$
