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}`
