các phương trình sau: a) 3x+1+(1/x-3)=2x+4+(1/x-3) b) 2(1-1,5x)=-3x c) 5x+3,48+2,6=2x+5+0,4x d) 4(12x+5)/12=3(2x-7)/12 e) Giải (2x-3/4)-(1-x/5)=1 f) 7

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1. Đáp án + Giải thích các bước giải:

   a)  `3x + 1 + 1/(x – 3) = 2x + 4 + 1/(x – 3) (x ne 3) <=> [3x(x – 3)]/(x – 3) + [1(x – 3)]/(x – 3) + 1/(x – 3) = [2x(x – 3)]/(x – 3) + [4(x – 3)]/(x – 3) + 1/(x – 3)` $\\$ `<=> [3x(x – 3) + 1(x – 3) + 1]/(x – 3) = [2x(x – 3) + 4(x – 3) + 1]/(x – 3)` $\\$ `<=> 3x(x – 3) + 1(x – 3) + 1 = 2x(x – 3) + 4(x – 3) + 1` $\\$ `<=> 3x^2 – 9x + x – 3 + 1 = 2x^2 – 6x + 4x – 12 + 1` $\\$ `<=> 3x^2 – 9x + x – 3 + 1 – 2x^2 + 6x – 4x + 12 – 1 = 0` $\\$ `<=> x^2-6x + 9 = 0 <=> (x – 3)^2 = 0 ` $\\$ `<=> x = 3(loại)`

   Vậy `S = emptyset`

   b) `2(1 – 1,5x) = -3x` $\\$ `<=> 2 – 3x = -3x` $\\$ ` <=> 2 – 3x + 3x = 0` $\\$ `<=> 2 + 0x = 0`$\\$ ` <=> 0x = -2`

   PT vô nghiệm 

   Vậy `S = emptyset`

   `c) 5x + 3,48 + 2,6 = 2x + 5 + 0,4x <=> 5x + 6,08 = 2,4x + 5` $\\$ `<=> 5x – 2,4x = 5 – 6,08 <=> 2,6x = -1,08 ` $\\$ `<=> x = (-1,08)/(2,6) = -27/65`

   Vậy `S = {-27/65}`

   `d) [4(12x + 5)]/12 = [3(2x – 7)]/12 <=> (48x + 20)/12 = (6x – 21)/12` $\\$ `<=> 48x + 20 = 6x – 21 <=> 48x – 6x = -21 – 20` $\\$ `<=> 42x = -41 <=> x = -41/42`

   Vậy `S = {-41/42}`

   `e) (2x – 3/4) – (1 – x/5) = 1 <=>[8x – 3]/4 – (5 – x)/5 = 1` $\\$ `<=> [5(8x – 3)]/20 – [4(5 – x)]/20 = 20/20` $\\$ `<=> 5(8x – 3) – 4(5 – x) = 20` $\\$ `<=> 40x – 15 – 20 + 4x = 20`$\\$ `<=> 44x – 35 = 20 <=> 44x = 55` $\\$ `<=> 4x = 5 <=> x = 5/4`

   Vậy `S = {5/4}`

   `f) [7(5x – 4)]/14 = [2(16x – 1)]/14 <=> (35x – 28)/14 = (32x – 2)/14` $\\$ `<=> 35x – 28 = 32x – 2 <=> 35x – 32x = -2 + 28` $\\$ `<=> 3x = 26 <=> x = 26/3`

   Vậy `S = {26/3}`

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