Đáp án + Giải thích các bước giải:
`a)` `3x(x - 2)=x^2-4` $\\$ `<=>3x(x - 2) = (x-2)(x+2)` $\\$ `<=>3x(x-2)-(x-2)(x+2)=0` $\\$ `<=>(x-2)[3x-(x+2)]=0 ` $\\$ `<=>(x-2)(3x-x-2)=0` $\\$ `<=> (x-2)(2x-2)=0` $\\$ `<=> (x-2)*2(x-1)=0<=> `\(\left[ \begin{array}{l}x=1\\x=2\end{array} \right.\)
Vậy `S={1;2}`
`b)` `(x + 3)/(x - 1) + x/(x+1)=(x^2+4x+5)/(x^2-1)(xnepm1)` $\\$ `<=>[(x+3)(x+1)+(x-1)x]/[(x-1)(x+1)]=(x^2+4x+5)/[(x-1)(x+1)]` $\\$ `=> (x + 3)(x + 1) + (x-1)x=x^2+4x+5` $\\$ `<=> x^2 + x + 3x +3 + x^2 - x - x^2 - 4x - 5 = 0` $\\$ `<=> x^2 -x-2=0` $\\$ `<=> x^2 + x - 2x - 2 = 0` $\\$ `<=> x(x + 1) - 2(x + 1) = 0` $\\$ `<=> (x + 1)(x - 2) = 0 <=> `\(\left[ \begin{array}{l}x=-1(ktm)\\x=2(tm)\end{array} \right.\)
Vậy `S={2}`
`c)` `3(x - 1) < 5(x + 1) -2` $\\$ `<=>3x-3<5x+5-2` $\\$ `<=>3x-3<5x+3` $\\$ `<=> 3x - 5x < 3 + 3` $\\$ `<=> -2x < 6` $\\$ `<=> x> -3`
Vậy `S={x|x> -3}`
`d)` `x^3 > -2x<=>x^3+2x>0` $\\$ `<=>x(x^2+2)>0` $\\$ `<=>x>0`
Vậy `S={x|x>0}`
