Đáp án:
`x=-5/4`
Giải thích các bước giải:
Có `x^6-1=(x^3-1)(x^3+1)=(x-1)(x+1)(x^2+x+1)(x^2-x+1)`
`=> (x+1)/(x^2+x+1) -(x-1)/(x^2-x+1)=(2(x+2)^2)/((x-1)(x+1)(x^2+x+1)(x^2-x+1))`
`<=>((x+1)(x^2-x+1)-(x-1)(x^2+x+1))/((x^2+x+1)(x^2-x+1))=(2(x+2)^2)/((x-1)(x+1)(x^2+x+1)(x^2-x+1))`
`<=>(x^3+1-x^3+1)/((x^2+x+1)(x^2-x+1))=(2(x+2)^2)/((x-1)(x+1)(x^2+x+1)(x^2-x+1))`
`<=>2/((x^2+x+1)(x^2-x+1))=(2(x+2)^2)/((x-1)(x+1)(x^2+x+1)(x^2-x+1))`
`<=>(2(x-1)(x+1))/((x^2+x+1)(x^2-x+1))=(2(x+2)^2)/((x-1)(x+1)(x^2+x+1)(x^2-x+1))`
`=>2(x^2-1)=2(x^2+4x+4)`
`<=>2x^2-2=2x^2+8x+8`
`<=>8x=-10`
`<=>x=-5/4`
Vậy `x=-5/4.`