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a: \(\dfrac{6}{5\sqrt{8}}=\dfrac{6}{10\sqrt{2}}=\dfrac{3}{5\sqrt{2}}=\dfrac{3\sqrt{2}}{10}\)
b: \(\dfrac{7}{5+2\sqrt{3}}=\dfrac{7\left(5-2\sqrt{3}\right)}{13}\)
c: \(\dfrac{6}{\sqrt{7}-\sqrt{5}}=\dfrac{6\left(\sqrt{7}+\sqrt{5}\right)}{2}=3\left(\sqrt{7}+\sqrt{5}\right)\)
a) \(\dfrac{6}{5\sqrt{8}}\)
\(=\dfrac{6}{5\cdot2\sqrt{2}}\)
\(=\dfrac{6}{10\sqrt{2}}\)
\(=\dfrac{3\sqrt{2}}{5\sqrt{2}\cdot\sqrt{2}}\)
\(=\dfrac{3\sqrt{2}}{10}\)
b) \(\dfrac{7}{5+2\sqrt{3}}\)
\(=\dfrac{7\left(5-2\sqrt{3}\right)}{\left(5+2\sqrt{3}\right)\left(5-2\sqrt{3}\right)}\)
\(=\dfrac{7\left(5-2\sqrt{3}\right)}{5^2-\left(2\sqrt{3}\right)^2}\)
\(=\dfrac{7\left(5-2\sqrt{3}\right)}{13}\)
\(=\dfrac{35-14\sqrt{3}}{13}\)
c) \(\dfrac{6}{\sqrt{7}-\sqrt{5}}\)
\(=\dfrac{6\left(\sqrt{7}+\sqrt{5}\right)}{\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)}\)
\(=\dfrac{6\left(\sqrt{7}+\sqrt{5}\right)}{2}\)
\(=3\sqrt{7}+3\sqrt{5}\)
a) `-2/(3\sqrt11) = (-2\sqrt11)/(3\sqrt11 .\sqrt11) =(-2\sqrt11)/(3.11)=(-2\sqrt11)/33`
b) `3/(\sqrt7+4) = (3.(\sqrt7-4))/((\sqrt7+4)(\sqrt7-4))`
`=(3.(\sqrt7-4))/((\sqrt7)^2-4^2)`
`=(3.(\sqrt7-4))/(-9)`
`=(4-\sqrt7)/3`
\(\dfrac{-2}{3\sqrt{11}}=\dfrac{-2\sqrt{11}}{33}\)
\(\dfrac{3}{4+\sqrt{7}}=\dfrac{12-3\sqrt{7}}{7}\)
a: \(\dfrac{\sqrt{5}}{\sqrt{7}}=\dfrac{\sqrt{5\cdot7}}{7}=\dfrac{\sqrt{35}}{7}\)
b: \(\dfrac{2}{\sqrt{a}-1}=\dfrac{2\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}=\dfrac{2\sqrt{a}+2}{a-1}\)
\(\dfrac{\sqrt{5}-1}{\sqrt{5}+1}=\dfrac{\left(\sqrt{5}-1\right)^2}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}=\dfrac{5-2\sqrt{5}+1}{5-1}=\dfrac{2\left(3-\sqrt{5}\right)}{4}=\dfrac{3-\sqrt{5}}{2}\)
b: \(\dfrac{37}{7+2\sqrt{3}}=7-2\sqrt{3}\)
c:\(=\dfrac{\sqrt{5}\left(2\sqrt{2}-\sqrt{5}\right)}{\sqrt{2}\left(2\sqrt{2}-\sqrt{5}\right)}=\sqrt{\dfrac{5}{2}}=\dfrac{\sqrt{10}}{2}\)
d: \(=\dfrac{\left(1+\sqrt{a}\right)\cdot\left(2+\sqrt{a}\right)}{4-a}\)
Bài 1:
a: \(\dfrac{2-\sqrt{3}}{3\sqrt{6}}=\dfrac{2\sqrt{6}-3\sqrt{2}}{18}\)
b: \(\dfrac{1}{\sqrt{2}+\sqrt{3}}=\sqrt{3}-\sqrt{2}\)
c: \(\dfrac{1}{2\sqrt{2}-3\sqrt{3}}=\dfrac{2\sqrt{2}+3\sqrt{3}}{8-27}=\dfrac{-2\sqrt{2}-3\sqrt{3}}{19}\)
d: \(\dfrac{2\sqrt{10}-5}{4-\sqrt{10}}=\dfrac{\sqrt{10}}{2}\)
e: \(\dfrac{37}{7+2\sqrt{3}}=7-2\sqrt{3}\)
(\(\sqrt{a}\)+\(\sqrt{b}\)+1) /\(\sqrt{a}+\sqrt{B}-1\).\(\sqrt{a}+\sqrt{b}+1\)=