`a) ((\sqrt{a}-\sqrt{b})^2+4\sqrt{ab})/(\sqrt{a}+\sqrt{b})` ĐK: `a,b>=0`
`=(a-2\sqrt{ab}+b+4\sqrt{ab})/(\sqrt{a}+\sqrt{b})`
`=(a+2\sqrt{ab}+b)/(\sqrt{a}+\sqrt{b})`
`=(\sqrt{a}+\sqrt{b})^2/(\sqrt{a}+\sqrt{b})`
`=\sqrt{a}+\sqrt{b}`
`b) (x+6\sqrt{x}+9)/(x-9)` ĐK: `x>=0; x \ne 9`
`=(\sqrt{x}+3)^2/((\sqrt{x}-3)(\sqrt{x}+3))`
`=(\sqrt{x}+3)/(\sqrt{x}-3)`
`c) ((1+\sqrt{x})^2-4\sqrt{x})/(1-\sqrt{x})` ĐK: `x>=0; x \ne 1`
`=(1+2\sqrt{x}+x-4\sqrt{x})/(1-\sqrt{x})`
`=(1-2\sqrt{x}+x)/(1-\sqrt{x})`
`=(1-\sqrt{x})^2/(1-\sqrt{x})`
`=1-\sqrt{x}`
`d) (x-y)/(\sqrt{x}-\sqrt{y})-((\sqrt{x})^3-(\sqrt{y})^3)/(x+\sqrt{xy}+y)-2y` ĐK: `x,y>=0; x \ne y`
`=((\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y}))/(\sqrt{x}-\sqrt{y})-((\sqrt{x}-\sqrt{y})(x+\sqrt{xy}+y))/(x+\sqrt{xy}+y)-2y`
`=\sqrt{x}+\sqrt{y}-\sqrt{x}+\sqrt{y}-2y`
`=2\sqrt{y}-2y`
`e) ((\sqrt{a}-\sqrt{b})^2+4\sqrt{ab})/(\sqrt{a}+\sqrt{b}) - (a\sqrt{b}-b\sqrt{a})/(\sqrt{ab})` ĐK: `a,b>=0`
`=\sqrt{a}+\sqrt{b}-(\sqrt{ab}(\sqrt{a}-\sqrt{b}))/(\sqrt{ab})`
(Phân thức 1 giống y sì câu a nên mình viết lại đáp án luôn ._.)
`=\sqrt{a}+\sqrt{b}-\sqrt{a}+\sqrt{b}`
`=2\sqrt{b}`
