Bài `1:`

$a)\dfrac{x^2-5}{x+sqrt{5}}$ `(x\ne-\sqrt{5})`

$=\dfrac{(x-\sqrt{5})(x+\sqrt{5})}{x+\sqrt{5}}$

$=x-\sqrt{5}$

$b)\dfrac{x^2+2\sqrt{2}x+2}{x^2-2}$ `(x\ne±\sqrt{2})`

$=\dfrac{(x+\sqrt{2})^2}{(x-\sqrt{2})(x+\sqrt{2})}$

$=\dfrac{x+\sqrt{2}}{x-\sqrt{2}}$

$c)\dfrac{x-\sqrt{xy}}{x-y}+\dfrac{\sqrt{y}}{\sqrt{x}+\sqrt{y}}$

$=\dfrac{x-\sqrt{xy}}{(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}+\dfrac{\sqrt{y}(\sqrt{x}-\sqrt{y})}{(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}$

$=\dfrac{x-\sqrt{xy}+\sqrt{xy}-y}{x-y}$

$=\dfrac{x-y}{x-y}$

$=1$

$d)\dfrac{\sqrt{a}-a}{\sqrt{a}-1}$

$=-\dfrac{\sqrt{a}(\sqrt{a}-1)}{\sqrt{a}-1}$

$=-\sqrt{a}$

$e)\dfrac{3+\sqrt{3}}{\sqrt{6}+\sqrt{2}}$

$=\dfrac{\sqrt{3}(\sqrt{3}+1)}{\sqrt{2}(\sqrt{3}+1)}$

$=\dfrac{\sqrt{3}}{\sqrt{2}}$

$g)\dfrac{x\sqrt{y}+y\sqrt{x}}{x+2\sqrt{xy}+y}$

$=\dfrac{\sqrt{xy}(\sqrt{x}+\sqrt{y})}{(\sqrt{x}+\sqrt{y})^2}$

$=\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}$

Hướng dẫn trả lời:

Bài 1:

a) `{x^2 - 5}/{x + sqrt{5}}` (`x ne - sqrt{5}`)

`= {x^2 - (sqrt{5})^2}/{x + sqrt{5}}`

`= {(x + sqrt{5})cdot(x - sqrt{5})}/{x + sqrt{5}}`

`= x - sqrt{5}`

b) `{x^2 + 2sqrt{2}x + 2}/{x^2 - 2}` (`x ne ± sqrt{2}`)

`= {x^2 + 2cdotxcdot sqrt{2} + (sqrt{2})^2}/{x^2 - (sqrt{2})^2}`

`= {(x + sqrt{2})^2}/{(x + sqrt{2})cdot(x - sqrt{2})}`

`= {x + sqrt{2}}/{x - sqrt{2}}`

c) `{x - sqrt{xy}}/{x - y} + {sqrt{y}}/{sqrt{x} + sqrt{y}}`

`= {x - sqrt{xy}}/{x - y} + {sqrt{y}cdot(sqrt{x} - sqrt{y})}/{(sqrt{x} + sqrt{y})cdot(sqrt{x} - sqrt{y})}`

`= {x - sqrt{xy}}/{x - y} + {sqrt{y}cdot(sqrt{x} - sqrt{y})}/{(sqrt{x})^2 - (sqrt{y})^2}`

`= {x - sqrt{xy}}/{x - y} + {sqrt{y}cdot(sqrt{x} - sqrt{y})}/{x - y}`

`= {x - sqrt{xy} + sqrt{y}cdot(sqrt{x} - sqrt{y})}/{x - y}`

`= {x - sqrt{xy} + sqrt{y}cdot sqrt{x} + sqrt{y}cdot(- sqrt{y})}/{x - y}`

`= {x - sqrt{xy} + sqrt{xy} - y}/{x - y}`

`= {x - y}/{x - y}`

`= 1`

d) `{sqrt{a} - a}/{sqrt{a} - 1}`

`= {sqrt{a} - (sqrt{a})^2}/{sqrt{a} - 1}`

`= {sqrt{a}cdot(1 - sqrt{a})}/{sqrt{a} - 1}`

`= {-sqrt{a}cdot(sqrt{a} - 1)}/{sqrt{a} - 1}`

`= - sqrt{a}`

e) `{3 + sqrt{3}}/{sqrt{6} + sqrt{2}}`

`= {(sqrt{3})^2 + sqrt{3}}/{sqrt{2}cdot sqrt{3} + sqrt{2}}`

`= {sqrt{3}cdot(sqrt{3} + 1)}/{sqrt{2}cdot(sqrt{3} + 1)}`

`= sqrt{3}/sqrt{2}`

g) `{xsqrt{y} + ysqrt{x}}/{x + 2sqrt{xy} + y}`

`= {sqrt{xy}cdot sqrt{x} + sqrt{xy}cdot sqrt{y}}/{(sqrt{x})^2 + 2cdot sqrt{x}cdot sqrt{y} + (sqrt{y})^2}`

`= {sqrt{xy}cdot(sqrt{x} + sqrt{y})}/{(sqrt{x} + sqrt{y})^2}`

`= sqrt{xy}/{sqrt{x} + sqrt{y}}`

Đáp án:

a) `= x - sqrt{5}`

b) `= {x + sqrt{2}}/{x - sqrt{2}}`

c) `= 1`

d) `= - sqrt{a}`

e) `= sqrt{3}/sqrt{2}`

g) `= sqrt{xy}/{sqrt{x} + sqrt{y}}`