Đáp án + Giải thích các bước giải:
1) Rút gọn :
`M = (1/(x + 1) + 2/(1-x) + x/(x^2-1)):1/(x + 1)(x ne pm 1)` $\\$ `= (1/(x+1) - 2/(x-1)+x/(x^2-1))*(x+1)` $\\$ `= ((x-1)/[(x-1)(x+1)] - [2(x+1)]/[(x-1)(x+1)]+x/[(x-1)(x+1)])*(x+1)` $\\$ `= (x - 1 - 2(x + 1) + x)/[(x+1)(x-1)]*(x+1)` $\\$ `= (x - 1 - 2x - 2 + x)/[(x-1)(x+1)]*(x+1)` $\\$ `= (-3)/[(x-1)(x+1)] * (x + 1) = [-3(x + 1)]/[(x-1)(x + 1)] = (-3)/(x-1)`
2) Với x = 2(tm) thì : `M = (-3)/(2-1)=(-3)/1=-3`
Câu 2 :
1) `4x + 11 = 2 - 5x <=>4x+5x=2-11` $\\$ `<=> 9x = -9 <=> x = -1`
Vậy `S={-1}`
2) `x/(x + 2) + 6/(x - 2) = (2x + 12)/(x^2 - 4)(x ne pm2)` $\\$ `<=> [x(x - 2)]/[(x-2)(x+2)] + [6(x+2)]/[(x-2)(x+2)] = (2x + 12)/[(x-2)(x+2)]` $\\$ `=> x(x - 2) + 6(x + 2) = 2x + 12` $\\$ `<=> x^2 - 2x + 6x + 12 - 2x - 12 = 0` $\\$ `<=> 3x + 0 = 0 <=> x = 0(TM)`
Vậy `S = {0}`
3) `|x - 3| = 4x + 9 (**)`
Ta có : `|x - 3| = x - 3` khi `x - 3>= 0 <=> x >= 3`
PT (*) trở thành : `x - 3 = 4x + 9 <=> x-4x=9+3<=>-3x=12<=>x=-4(KTM)`
`|x - 3| = -(x - 3)` khi `x - 3 < 0 <=> x < 3`
PT (*) trở thành :`-(x - 3)=4x+9<=>-x+3=4x+9<=>-x-4x=9-3` $\\$ `<=> -5x=6<=>x=-6/5(TM)`
Vậy `S = {-6/5}`
4) `2 + [3(x+1)]/2 <= 3 - (x - 1)/4` $\\$ `<=> 2*4+4*[3(x+1)]/2<=3*4-4*(x-1)/4` $\\$ `<=> 8 + 2[3(x + 1)] <= 12 - (x - 1)` $\\$ `<=> 8 + 2(3x + 3) <= 12 - x + 1` $\\$ `<=> 8 + 6x + 6 <= 12 - x + 1` $\\$ `<=> 8 + 6x + 6 - 12 + x <= 1` $\\$ `<=>2 + 7x <= 1 ` $\\$ `<=> 7x <= -1` $\\$ `<=> x <= -1/7`
Vậy `S = {x|x <= -1/7}`
