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

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1. 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)`

   Giải thích các bước giải:

    

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2. `1/(x-1) + 2/(x-2) + 3/(x-3) = 6/(x-6)`

    ĐKXĐ : `x \ne 1 , x \ne 2 , x \ne 3 , x \ne 6`

   `⇔ (1(x-2)(x-3)(x-6)+2(x-1)(x-3)(x-6)+3(x-1)(x-2)(x-6))/((x-1)(x-2)(x-3)(x-6)) = (6(x-1)(x-2)(x-3))/((x-1)(x-2)(x-3)(x-6)`

   `⇔ (x-2)(x-3)(x-6) + 2(x-1)(x-3)(x-6) + 3(x-1)(x-2)(x-6) = 6(x-1)(x-2)(x-3)`

   `⇔ -22x^2 + 84x – 72 = 0`

   `⇔ 11x^2 – 42x + 36= 0`

   `⇔ x^2 – 42/11x + 36/11 = 0`

   `⇔ [x^2 – 14.x.(3.7)/11 + (3/11)^2] – 5/11 = 0`

   `⇔ (x-(3.7)/11)^2 = 5/11`

   `⇔ x – (3.7)/11 = (\pm\sqrt{5})/11`

   `⇔ x = (3(7\pm\sqrt{5}))/11`

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