Đáp án + Giải thích các bước giải:
`a) (3x-2)/(x-1) - (x+3)/(x+1) = 2`
ĐKXĐ : \(\left\{ \begin{array}{l}x-1\ne0\\x+1\ne0\end{array} \right.\) `=>` \(\left\{ \begin{array}{l}x\ne1\\x\ne-1\end{array} \right.\)
`⇔ ((3x-2)(x+1))/((x-1)(x+1)) - ((x+3)(x-1))/((x-1)(x+1)) = 2(x-1)(x+1)`
`⇒ (3x-2)(x+1) - (x+3)(x-1) = 2(x-1)(x+1)`
`⇔ 2x^2 - x + 1 = 2x^2 - 2`
`⇔ 2x^2 - x = 2x^2 - 3`
`⇔ -x = -3`
`⇔ x = 3(TM)`
Vậy `S = {3}`
`b) 4x^2 - 1 = (x-5)(1-2x)`
`⇔ 4x^2 - 1 = -2x^2 + 11x - 5`
`⇔ -2x^2 + 11x - 5 = 4x^2 - 1`
`⇔ -2x^2 + 11x - 4 = 4x^2`
`⇔ -6x^2 + 11x - 4 = 0`
`⇔ -(6x^2-11x+4) = 0`
`⇔ -(2x-1)(3x-4) = 0`
`⇔`\(\left[ \begin{array}{l}2x-1=0\\3x-4=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=\dfrac{4}{3}\end{array} \right.\)
Vậy `S = {1/2,4/3}`
`c) (x-3)/3 - (2x-1)/2 > 2`
`⇔ (2(x-3))/6 - (3(2x-1))/6 > 2*6`
`⇒ 2(x-3) - 3(2x-1) > 12`
`⇔ -4x - 3 > 12`
`⇔ -4x > 15`
`⇔ 4x < -15`
`⇔ x < (-15)/4`
Vậy `S = {x|x< (-15)/4}`
