3:
\(C_3=\left(1+\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(1-\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\right)\)
\(=\left(1+\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\left(1-\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\)
\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)\)
=1-a
4: \(C=\left(\dfrac{a-\sqrt{a}}{\sqrt{a}-1}+2\right)\left(2-\dfrac{a+\sqrt{a}}{1+\sqrt{a}}\right)\)
\(=\left(\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}+2\right)\left(2-\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\)
\(=\left(2+\sqrt{a}\right)\left(2-\sqrt{a}\right)=4-a\)
5: \(C_5=\left(2-\dfrac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\left(2-\dfrac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)\)
\(=\left(2-\dfrac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}-3}\right)\left(2+\dfrac{\sqrt{a}\left(\sqrt{b}-5\right)}{\sqrt{b}-5}\right)\)
\(=\left(2-\sqrt{a}\right)\left(2+\sqrt{a}\right)=4-a\)
6: Sửa đề: \(C_6=\left(3+\dfrac{a-2\sqrt{a}}{\sqrt{a}-2}\right)\left(3-\dfrac{3a+\sqrt{a}}{3\sqrt{a}+1}\right)\)
\(=\left(3+\dfrac{\sqrt{a}\left(\sqrt{a}-2\right)}{\sqrt{a}-2}\right)\left(3-\dfrac{\sqrt{a}\left(3\sqrt{a}+1\right)}{3\sqrt{a}+1}\right)\)
\(=\left(3-\sqrt{a}\right)\left(3+\sqrt{a}\right)=9-a\)