Hướng dẫn trả lời:
1)
a) `{x - 5}/{2sqrt{x} + 2sqrt{5}} + sqrt{5}` (đk: `x > 0`)
`= {(sqrt{x})^2 - (sqrt{5})^2}/{2cdot(sqrt{x} + sqrt{5})} + sqrt{5}`
`= {(sqrtx - sqrt5)cdot(sqrt{x} + sqrt{5})}/{2cdot(sqrt{x} + sqrt{5})} + sqrt{5}`
`= {sqrtx - sqrt5}/{2} + sqrt{5}`
`= {sqrtx - sqrt5}/{2} + {2sqrt{5}}/2`
`= {sqrtx - sqrt 5 + 2sqrt{5}}/2`
`= {sqrtx + sqrt{5}}/2`
b) Đề thiếu. Bạn xem lại đề nhé.
c) `{3 - 2sqrt{2}}/{sqrt{2} - 1} - sqrt{2}`
`= {2 - 2sqrt{2} + 1}/{sqrt{2} - 1} - sqrt{2}`
`= {(sqrt{2})^2 - 2cdot sqrt{2}cdot1 + 1^2}/{sqrt{2} - 1} - sqrt{2}`
`= {(sqrt{2} - 1)^2}/{sqrt{2} - 1} - sqrt{2}`
`= (sqrt{2} - 1) - sqrt{2}`
`= sqrt{2} - 1 - sqrt{2}`
`= (sqrt{2} - sqrt{2}) - 1`
`= - 1`
d) `{7 + 2sqrt{6}}/{1 + sqrt{6}}`
`= {1 + 2sqrt{6} + 6}/{1 + sqrt{6}}`
`= {1^2 + 2cdot1cdot sqrt{6} + (sqrt{6})^2}/{1 + sqrt{6}}`
`= {(1 + sqrt{6})^2}/{1 + sqrt{6}}`
`= 1 + sqrt{6}`
2)
a) `3sqrt{3} - 6sqrt{2} - 4/3sqrt{3} + 1/2sqrt{2} + 18/6sqrt{2}`
`= 3sqrt{3} - 6sqrt{2} - 4/3sqrt{3} + 1/2sqrt{2} + 3sqrt{2}`
`= (3sqrt{3} - 4/3sqrt{3}) + (- 6sqrt{2} + 1/2sqrt{2} + 3sqrt{2})`
`= 5/3sqrt{3} - 5/2sqrt{2}`
b) `{1 - (sqrt{5})^2}/{1 + sqrt{5}}`
`= {1^2 - (sqrt{5})^2}/{1 + sqrt{5}}`
`= {(1 - sqrt{5})cdot(1 + sqrt{5})}/{1 + sqrt{5}}`
`= 1 - sqrt{5}`
c) `2/3sqrt{5} - 3/4sqrt{3} + 7/3sqrt{5} + 6/8sqrt{3}`
`= 2/3sqrt{5} - 3/4sqrt{3} + 7/3sqrt{5} + 3/4sqrt{3}`
`= (2/3sqrt{5} + 7/3sqrt{5}) + (- 3/4sqrt{3} + 3/4sqrt{3})`
`= 9/3sqrt{5}`
`= 3sqrt{5}`
d) `{2}/{sqrt{2}} + 3/{sqrt{3}} - sqrt{3}`
`= {(sqrt{2})^2}/{sqrt{2}} + {(sqrt3)^2}/{sqrt{3}} - sqrt{3}`
`= sqrt{2} + sqrt{3} - sqrt{3}`
`= sqrt{2}`
