\(\begin{array}{l}
a)\quad \dfrac{1}{\sqrt x-1} - \dfrac{1}{1+\sqrt x} + 1\quad (x>0; x\ne 1)\\
= \dfrac{\sqrt x +1 - \left(\sqrt x - 1\right)}{\left(\sqrt x - 1\right)\left(\sqrt x + 1\right)} + \dfrac{\left(\sqrt x - 1\right)\left(\sqrt x + 1\right)}{\left(\sqrt x - 1\right)\left(\sqrt x + 1\right)}\\
= \dfrac{2 + (x -1)}{\left(\sqrt x - 1\right)\left(\sqrt x + 1\right)}\\
= \dfrac{x+1}{x-1}\\
b)\quad \dfrac{1}{\sqrt x+2} - \dfrac{2}{\sqrt x-2} -\dfrac{\sqrt x}{4-x}\quad (x>0;x\ne 4)\\
=\dfrac{\sqrt x - 2 - 2\left(\sqrt x + 2\right) + \sqrt x}{\left(\sqrt x - 2\right)\left(\sqrt x + 2\right)}\\
= - \dfrac{6}{x-4}\\
\end{array}\)
