6:
a: \(Q=\dfrac{\sqrt{x}-2+7}{x-4}:\dfrac{\sqrt{x}-1-\sqrt{x}+2}{\sqrt{x}-2}\)
\(=\dfrac{\sqrt{x}+5}{x-4}\cdot\dfrac{\sqrt{x}-2}{1}=\dfrac{\sqrt{x}+5}{\sqrt{x}+2}\)
b:
1: \(x=5+\sqrt{2}-4-\sqrt{2}=1\)
Khi x=1 thì \(Q=\dfrac{1+5}{1+2}=\dfrac{6}{3}=2\)
2: \(x=\sqrt{2\left(2+\sqrt{3}\right)}-\sqrt{2\left(2-\sqrt{3}\right)}\)
\(=\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}=2\)
Khi x=2 thì \(Q=\dfrac{5+\sqrt{2}}{2+\sqrt{2}}=\dfrac{8-3\sqrt{2}}{2}\)
3:
a: \(P=\left(\dfrac{2\left(\sqrt{3}+1\right)}{2}-\dfrac{3\left(2+\sqrt{3}\right)}{4-3}+\dfrac{15\left(3+\sqrt{3}\right)}{6}\right)\cdot\dfrac{1}{5+\sqrt{3}}\)
\(=\left(\sqrt{3}+1-6-3\sqrt{3}+\dfrac{15}{2}+\dfrac{5}{2}\sqrt{3}\right)\cdot\dfrac{1}{5+\sqrt{3}}\)
\(=\left(\dfrac{11}{2}\sqrt{3}+\dfrac{5}{2}\right)\cdot\dfrac{1}{5+\sqrt{3}}=\dfrac{11\sqrt{3}+5}{2\left(5+\sqrt{3}\right)}=\dfrac{25\sqrt{3}-4}{22}\)
b:
\(Q=\left(-\dfrac{\sqrt{7}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}-\dfrac{\sqrt{5}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}\right)\cdot\left(\sqrt{7}-\sqrt{5}\right)\)
=(-căn 7-căn 5)(căn 7-căn 5)
=-(căn 7+căn 5)(căn 7-căn 5)
=-(7-5)=-2
