\(\left(\dfrac{\sqrt{a}+2}{a+2\sqrt{a}+1}-\dfrac{\sqrt{a}-2}{a-1}\right)\cdot\dfrac{\sqrt{a}+1}{a}\)
\(=\left(\dfrac{\left(\sqrt{a}+2\right)}{\left(\sqrt{a}+1\right)^2}-\dfrac{\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\cdot\dfrac{\sqrt{a}+1}{a}\)
\(=\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)-\left(\sqrt{a}-2\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+1\right)^2\cdot\left(\sqrt{a}-1\right)}\cdot\dfrac{\sqrt{a}+1}{a}\)
\(=\dfrac{a+\sqrt{a}-2-\left(a-\sqrt{a}-2\right)}{a-1}\cdot\dfrac{1}{a}\)
\(=\dfrac{2\sqrt{a}}{a\left(a-1\right)}=\dfrac{2}{\sqrt{a}\left(a-1\right)}\)
\(\left(\dfrac{1-x\sqrt{x}}{1-\sqrt{x}}\right)\cdot\left(\dfrac{1-\sqrt{x}}{1-x}\right)^2\)
\(=\left(\dfrac{\left(1-\sqrt{x}\right)\left(1+x+\sqrt{x}\right)}{1-\sqrt{x}}\right)\cdot\left(\dfrac{1}{1+\sqrt{x}}\right)^2\)
\(=\dfrac{x+\sqrt{x}+1}{\left(\sqrt{x}+1\right)^2}\)
