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Câu `1`
`a)` `P = \frac{1}{\sqrt{5} - 2} + \frac{1}{\sqrt{5}+2}`
`= \frac{\sqrt{5} + 2}{(\sqrt{5} - 2)(\sqrt{5} + 2)} + \frac{\sqrt{5} - 2}{(\sqrt{5} - 2)(\sqrt{5} + 2)}`
`= \frac{\sqrt{5} + 2 + \sqrt{5} - 2}{(\sqrt{5})^2 - 2^2} `
`= \frac{2\sqrt{5} }{5 -4 } `
`=2\sqrt{5}`
`b)` `Q =(1 + \frac{\sqrt{x}+1}{\sqrt{x}-1}) . \frac{1}{\sqrt{x}}`
`= (\frac{\sqrt{x}-1}{\sqrt{x}-1} + \frac{\sqrt{x}+1}{\sqrt{x}-1}) . \frac{1}{\sqrt{x}}`
`= \frac{\sqrt{x}-1+\sqrt{x}+1}{\sqrt{x}-1} . \frac{1}{\sqrt{x}}`
`= \frac{2\sqrt{x}}{\sqrt{x}-1} . \frac{1}{\sqrt{x}}`
`= \frac{2}{\sqrt{x}-1} `
Câu `2`
`a)` `(\sqrt{2}-1) . \frac{2 + \sqrt{2}}{2\sqrt{2}}`
`= (\sqrt{2}-1) . \frac{\sqrt{2}(\sqrt{2} +1)}{2\sqrt{2}}`
`= \frac{(\sqrt{2} +1)(\sqrt{2}-1) }{2}`
`= \frac{(\sqrt{2})^2 -1^2 }{2}`
`= \frac{1}{2}`
`b)` `Q = (\frac{1}{\sqrt{x}-3} + \frac{1}{\sqrt{x}+3} ) . (1 - \frac{3}{\sqrt{x}})`
`= (\frac{\sqrt{x}+3}{(\sqrt{x}-3)(\sqrt{x}+3)} + \frac{\sqrt{x}-3}{(\sqrt{x}-3)(\sqrt{x}+3)} ) . (1 - \frac{3}{\sqrt{x}})`
`= \frac{\sqrt{x}+3 +\sqrt{x}-3}{(\sqrt{x}-3)(\sqrt{x}+3)} . \frac{\sqrt{x}-3}{\sqrt{x}})`
`= \frac{2\sqrt{x}}{(\sqrt{x}-3)(\sqrt{x}+3)} . \frac{\sqrt{x}-3}{\sqrt{x}}`
`= \frac{2}{\sqrt{x}+3} `
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