10: \(\dfrac{a-2\sqrt{a}+1}{\sqrt{a}-1}+1\)
\(=\sqrt{a}-1+1\)
\(=\sqrt{a}\)
10)\(=\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}-1}+1=\sqrt{a}-1+1=\sqrt{a}\)
11)\(=2-\dfrac{\left(2\sqrt{a}+1\right)^2}{2\sqrt{a}+1}=2-2\sqrt{a}+1=1-2\sqrt{a}\)
23)\(=\dfrac{1}{1+\sqrt{5}}+\dfrac{1}{1-\sqrt{5}}=\dfrac{1-\sqrt{5}+1+\sqrt{5}}{\left(1+\sqrt{5}\right)\left(1-\sqrt{5}\right)}=\dfrac{2}{1^2-\left(\sqrt{5}\right)^2}=-\dfrac{1}{2}\)
25)\(=\dfrac{2}{2+\sqrt{3}}-\dfrac{2}{2-\sqrt{3}}=\dfrac{4-2\sqrt{3}-4-2\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}=\dfrac{-4\sqrt{3}}{2^2-\left(\sqrt{3}\right)^2}=4\sqrt{3}\)
25)\(\dfrac{2}{2+\sqrt{3}}-\dfrac{2}{2-\sqrt{3}}=\dfrac{2\left(2-\sqrt{3}\right)-2\left(2+\sqrt{3}\right)}{1}=-4\sqrt{3}\)
26)\(\dfrac{b-16}{\sqrt{b}-4}+2+\dfrac{b}{\sqrt{b}}=\sqrt{b}+4+2+\sqrt{b}=6+2\sqrt{b}\)
19)\(=\dfrac{6-a}{\sqrt{6}+\sqrt{a}}=\dfrac{\left(\sqrt{6}+\sqrt{a}\right)\left(\sqrt{6}-\sqrt{a}\right)}{\sqrt{6}+\sqrt{a}}=\sqrt{6}-\sqrt{a}\)
22)\(1-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}=\dfrac{1+\sqrt{5}}{1+\sqrt{5}}-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}=\dfrac{1+\sqrt{5}-5-\sqrt{5}}{1+\sqrt{5}}=-\dfrac{4}{1+\sqrt{5}}\)
22)\(1-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}=1-\sqrt{5}\)
19)\(\dfrac{6-a}{\sqrt{6}+\sqrt{a}}=\sqrt{6}-\sqrt{a}\)
17)\(\dfrac{3\sqrt{2}-6}{\sqrt{2}-1}+\dfrac{1}{2}=\dfrac{3\sqrt{2}\left(1-\sqrt{2}\right)}{\sqrt{2}-1}+\dfrac{1}{2}=\dfrac{1}{2}-3\sqrt{2}\)