Đáp án:
`2/(x - 1) = 3 + 1/(x + 2)` `(ĐKXĐ : x ne 1, -2)`
` <=> 2/(x - 1) = (3x + 6 + 1)/(x + 2)`
`<=> 2/(x - 1) = (3x + 7)/(x + 2)`
`<=> 2/(x - 1) - (3x + 7)/(x + 2) = 0`
`<=> [2(x + 2) - (3x + 7)(x - 1)]/[(x - 1)(x + 2)] = 0`
`<=> 2(x + 2) - (3x + 7)(x - 1) = 0`
`<=> 2x + 4 - (3x^2 + 7x - 3x - 7) = 0`
`<=> 2x + 4 - 3x^2 - 4x + 7 = 0`
`<=> -3x^2 - 2x + 11 = 0`
`<=> 3x^2 + 2x - 11 = 0`
`<=> 3(x^2 + 2/3 x - 11/3) = 0`
`<=> 3(x^2 + 2.x . 1/3 + 1/9 - 34/9) = 0`
`<=> 3(x + 1/3)^2 - 34/3 = 0`
`<=> 3(x + 1/3)^2 = 34/3`
`<=> (x + 1/3)^2 = 34/9`
`<=> x + 1/3 = ± \sqrt{34}/3`
`<=> x = ± \sqrt{34}/3 - 1/3`
Giải thích các bước giải:
