Đáp án + Giải thích các bước giải:
`a) 1/(x - 1) - (2x^2 - 5)/(x^3 - 1) = 4/(x^2 + x + 1) (x ne 1)` $\\$ `<=> 1/(x - 1) - (2x^2 - 5)/[(x - 1)(x^2 + x + 1)] = 4/(x^2 + x + 1)` $\\$ `<=> (2x^2 - 5)/[(x - 1)(x^2 + x + 1)] = 1/(x - 1) - 4/(x^2 + x + 1)` $\\$ `<=> (2x^2 - 5)/[(x - 1)(x^2 + x + 1)] = [1(x^2 + x + 1)]/[(x - 1)(x^2 + x + 1)] - [4(x - 1)]/[(x - 1)(x^2 + x + 1)` $\\$ `<=> (2x^2 - 5)/[(x - 1)(x^2 + x + 1)] = [x^2 + x + 1 - 4(x - 1)]/[(x - 1)(x^2 + x + 1)` $\\$ `<=> 2x^2 - 5 = x^2 + x + 1 - 4(x - 1)` $\\$ `<=> 2x^2 - 5 = x^2 + x + 1 - 4x + 4` $\\$ `<=> 2x^2 - 5 - x^2 - x - 1 + 4x - 4 = 0` $\\$ `<=> x^2+3x-10 = 0` $\\$ `<=> x^2 - 2x + 5x - 10 = 0` $\\$ `<=> x(x - 2) + 5(x - 2) = 0 <=> (x - 2)(x + 5) = 0` $\\$ `<=>` \(\left[ \begin{array}{l}x=2\\x=-5\end{array} \right.\)`(tm)`
Vậy S = {2;-5}
b) |2x + 3| = 2x + 2
Trường hợp 1 : 2x + 3 = 2x + 2
<=> 2x - 2x = 2 - 3 <=> 0x = -1 <=> pt vô nghiệm
Trường hợp 2 : -(2x + 3) = 2x + 2
<=> -2x - 3 - 2x - 2 = 0 <=> -4x - 5 = 0 <=> -4x = 5 <=> `x = -5/4`
Vậy `S = {-5/4}`
Vậy S = {-2,9}
c) `(x + 5)/2 - (3x - 6)/3 = 4 <=> [6(x + 5)]/12 - [4(3x - 6)]/12 = 48/12 ` $\\$ `<=> 6(x + 5) - 4(3x - 6) = 48` $\\$ `<=> 6x + 30 - 12x + 24 = 48` $\\$ `<=> -6x + 54 = 48 <=> -6x = -6 ` $\\$ `<=> x = 1`
Vậy S = {1}
