Đáp án+Giải thích các bước giải:
`M=(x+\root{3}{x}-2)/(x-1)-1/(\root{3}{x^2}+\root{3}{x}+1)+1/(\root{3}{x}-1)(x\ne1)`
`x-1=\root{3}{x^3}-1`
`x-1=(\root{3}{x}-1)(\root{3}{x^2}+\root{3}{x}+1)`
`=>M=(x+\root{3}{x}-2)/((\root{3}{x}-1)(\root{3}{x^2}+\root{3}{x}+1))-(\root{3}{x}-1)/((\root{3}{x}-1)(\root{3}{x^2}+\root{3}{x}+1))+(\root{3}{x^2}+\root{3}{x}+1)/((\root{3}{x}-1)(\root{3}{x^2}+\root{3}{x}+1))`
`M=(x+\root{3}{x}-2-\root{3}{x}+1+\root{3}{x^2}+\root{3}{x}+1)/((\root{3}{x}-1)(\root{3}{x^2}+\root{3}{x}+1))`
`M=(x+\root{3}{x^2}+\root{3}{x})/((\root{3}{x}-1)(\root{3}{x^2}+\root{3}{x}+1))`
`M=(\root{3}{x}(\root{3}{x^2}+\root{3}{x}+1))/((\root{3}{x}-1)(\root{3}{x^2}+\root{3}{x}+1))`
`M=(\root{3}{x})/(\root{3}{x}-1)`
`b)M=1/3`
`<=>(\root{3}{x})/(\root{3}{x}-1)=1/3`
`<=>3\root{3}{x}=\root{3}{x}-1`
`<=>2\root{3}{x}=-1`
`<=>8.x=-1`
`<=>x=-1/8`
Vậy `x=-1/8` thì `M=1/3.`
