Đáp án:
d) `(\sqrt{a}-\sqrt{b})/(\sqrt{ab}-1`
e) ` -(\sqrt{3}+\sqrt{6}-\sqrt{2}-2)`
f) `1+\sqrt2`
Giải thích các bước giải:
d) `(\sqrt{a}+a\sqrt{b}-\sqrt{b}-b\sqrt{a})/(ab-1)`
`= (\sqrt{a}(1+\sqrt{ab})-\sqrt{b}(1+\sqrt{ab}))/((\sqrt{ab}-1)(\sqrt{ab}+1)`
`= ((1+\sqrt{ab})(\sqrt{a}-\sqrt{b}))/((\sqrt{ab}-1)(\sqrt{ab}+1)`
`= (\sqrt{a}-\sqrt{b})/(\sqrt{ab}-1`
e) `(2\sqrt{15}-2\sqrt{10}+\sqrt{6}-3)/(2\sqrt{5}-2\sqrt{10}-\sqrt{3}+\sqrt{6}`
`=(2\sqrt{5}(\sqrt{3}-\sqrt{2}) - \sqrt{3}(\sqrt{3}-\sqrt{2}))/(2\sqrt{5}(1-\sqrt{2})-\sqrt{3}(1-\sqrt{2})`
`= ((\sqrt{3}-\sqrt{2})(2\sqrt{5}-\sqrt{3}))/((1-\sqrt{2})(2\sqrt{5}-\sqrt{3})`
`= (\sqrt{3}-\sqrt{2})/(1-\sqrt{2}) = ((\sqrt{3}-\sqrt{2})(1+\sqrt{2}))/(1-2)`
`= -(\sqrt{3}+\sqrt{6}-\sqrt{2}-2)`
f) `(\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16})/(\sqrt{2}+\sqrt{3}+\sqrt{4})`
`= (\sqrt2 + \sqrt3+\sqrt6 + 2\sqrt2+4)/(\sqrt2+\sqrt3+\sqrt4)`
`=((\sqrt{2}+\sqrt{3}+\sqrt4)+\sqrt{2}(\sqrt2+\sqrt3+\sqrt4))/(\sqrt2+\sqrt{3}+\sqrt4)`
`= ((\sqrt2+\sqrt3+\sqrt4)(1+\sqrt2))/(\sqrt2+\sqrt3+\sqrt4)=1+\sqrt2`
