Đáp án + Giải thích các bước giải:
`a) (2x - 5)/(x + 5) = 3 (x ne - 5) <=> (2x - 5)/(x + 5) = [3(x + 5)]/(x + 5)` $\\$ `<=> 2x - 5 = 3(x + 5) <=> 2x - 5 = 3x + 15` $\\$ `<=> 2x - 5 - 3x - 15 = 0 <=> -x - 20 = 0 ` $\\$ `<=> -x = 20 <=> x = -20(tm)`
Vậy `S = {-20}`
`b) (x^2 - 6)/x = x + 3/2 ( x ne 0) => (x^2 - 6)/x = (2x + 3)/2 <=> 2(x^2 - 6) = x(2x + 3) ` $\\$ `<=> 2x^2 - 12 = 2x^2 + 3x <=> 2x^2 - 12 - 2x^2 - 3x = 0` $\\$ `<=> -12 - 3x = 0 <=> x = -12/3 = -4(tm)`
Vậy `S = {-4}`
`c) [(x^2 + 2x) - (3x + 6)]/(x - 3) = 0 (x ne 3)` $\\$ `<=> [x(x + 2) - 3(x + 2)]/(x - 3) = 0 <=> [(x + 2)(x - 3)]/(x - 3) = 0` $\\$ `<=> x + 2 = 0 <=> x = -2(tm)`
Vậy `S = {-2}`
`d) 5/(3x + 2) = 2x - 1 ( x ne -2/3) <=> 5/(3x + 2) = [(2x - 1)(3x + 2)]/(3x + 2)` $\\$ `<=> (2x - 1)(3x + 2) = 5 <=> 6x^2 + 4x - 3x - 2 = 5` $\\$ `<=> 6x^2 + x = 7 <=> 6x^2 + x - 7 = 0 <=> 6x^2 - 6x + 7x - 7 = 0` $\\$ `<=> 6x(x - 1) + 7(x - 1) = 0 <=> (x - 1)(6x + 7) = 0` $\\$ `<=> `\(\left[ \begin{array}{l}x=1\\x=\frac{-7}{6}\end{array} \right.\) `(tm)`
Vậy `S = {1;-7/6}`
