Giải pt :( $\frac{1}{x-1}$ + $\frac{2}{x-2}$+ $\frac{3}{x-3}$= $\frac{6}{x-6}$

Đáp án:

`1/(x – 1)` + `2/(x – 2)` + `3/(x – 3)` = `6/(x – 6)` 

⇔` 1/(x – 1)` – `1/(x – 6)` + `2[1/(x – 2) – 1/(x – 6)]` + `3[1/(x – 3) – 1/(x – 6)]` = `0`

⇔ `- 5/[(x – 1)(x – 6)]` – `8/[(x – 2)(x – 6)]` – `9/[(x – 3)(x – 6)]` = `0`

⇔  `- 1/{(x – 6)[5/(x – 1) + 8/(x – 2) + 9/(x – 3)]}` = `0`

⇔ `5/(x – 1)` + `8/(x – 2)` + `9/(x – 3)` = `0`

⇔ $\text{5(x – 2)(x – 3) + 8(x – 3)(x – 1) + 9(x – 1)(x – 2) = 0}$

⇔ $\text{5(x² – 5x + 6) + 8(x² – 4x + 3) + 9(x² – 3x + 2) = 0}$

⇔ $\text{22x² – 84x + 72 = 0}$

⇔ $\text{11x² – 42x + 36 = 0 chia vế cho 2}$ 

⇔ `(21 + 3√5)/(11)` hoặc `(21 – 3√5)/(11)`

⇔ `[3(7 + √5)]/(11)` hoặc `[3(7 – √5)]/(11)`

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