`\qquad M=(\sqrt{x}/(\sqrt{x}-2)-4/(x-2\sqrt{x})).(1/(\sqrt{x}+2)+4/(x-2))`
`a)` ĐKXĐ: `{(x>=0),(\sqrt{x}-2\ne0),(x-2\sqrt{x}\ne0),(\sqrt{x}+2\ne0AAx),(x-2\ne0):}<=>{(x>=0),(\sqrt{x}\ne2),(\sqrt{x}\ne0),(x\ne2):}<=>{(x>0),(x\ne4),(x\ne2):}`
Vậy `x>0;x\ne4;x\ne2` thì M xác định
`b)` Với `x>0;x\ne4;x\ne2` thì
`M=(\sqrt{x}.\sqrt{x}-4)/(\sqrt{x}(sqrt{x}-2)).(x-2+4(\sqrt{x}+2))/((\sqrt{x}+2)(x-2))`
`M=(x-4)/(\sqrt{x}(\sqrt{x}-2)).(x-2+4\sqrt{x}+8)/((\sqrt{x}+2)(x-2)`
`M=((\sqrt{x}-2)(\sqrt{x}+2).(x+4\sqrt{x}+6))/(\sqrt{x}(\sqrt{x}-2)(\sqrt{x}+2)(x-2))`
`M=(x+4\sqrt{x}+6)/(x\sqrt{x}-2\sqrt{x})`
Vậy `M=(x+4\sqrt{x}+6)/(x\sqrt{x}-2\sqrt{x})` với `x>0;x\ne4;x\ne2`.
