Đáp án:

Giải thích các bước giải:

`N) (x+1)/65 + (x+2)/64 = (x+3)/63 + (x+4)/62`

`⇔ (x+1)/65 + 1 + (x+2)/64 + 1 = (x+3)/63 + 1 + (x+4)/62 + 1`

`⇔ (x+1+65)/65 + (x+2+64)/64 = (x+3+63)/63 + (x+4+62)/62`

`⇔ (x+66)/65 + (x+66)/64 = (x+66)/63 + (x+66)/62`

`⇔ (x+66)/65 + (x+66)/64 - (x+66)/63 - (x+66)/62`

`⇔ (x+66)(1/65 + 1/64 - 1/63 - 1/62)=0`

Vì `1/65 + 1/64 - 1/63 - 1/62 ne 0`

`⇒ x+66=0`

`⇔ x=-66`

Vậy `S={-66}`

`O) (x-12)/77 + (x-11)/78 = (x-74)/15 + (x-73)/16`

`⇔ (x-12)/77 - 1 + (x-11)/78 - 1 = (x-74)/15 - 1 + (x-73)/16 - 1`

`⇔ (x-12-77)/77 + (x-11-78)/78 = (x-74-15)/15 + (x-73 - 16)/16`

`⇔ (x-89)/77 + (x-89)/78 = (x-89)/15 + (x-89)/16`

`⇔ (x-89)/77 + (x-89)/78 - (x-89)/15 - (x-89)/16=0`

`⇔ (x-89)(1/77 + 1/78 - 1/15 - 1/16)=0`

Vì `1/77 + 1/78 - 1/15 - 1/16 ne0`

`⇒ x-89=0`

`⇒x=89`

Vậy `S={89}`

`G) (x+4)/5 - x + 4 = x/3 - (x-2)/2`

`⇔ (6(x+4))/30 - (30x)/30 + 120/30 = (10x)/30 - (15(x-2))/30`

`⇔ 6(x+4) - 30x + 120 = 10x - 15(x-2)`

`⇔ 6x+24-30x + 120 = 10x - 15x + 30`

`⇔ -24x + 144 + 5x - 30=0`

`⇔ -19x +114=0`

`⇔ -19x = -114`

`⇔ x=6`

Vậy `S={6}`

`h) 1/2 (x+1) + 1/4(x+3) = 3 - 1/3(x+2)`

`⇔ 1/2 x + 1/2 + 1/4 x + 3/4 = 3 - 1/3 x - 2/3`

`⇔ 3/4 x + 5/4 = 7/3 - 1/3 x`

`⇔ 3/4 x + 5/4 - 7/3 + 1/3 x = 0`

`⇔ 13/12 x + -13/12=0`

`⇔ 13/12 x = 13/12`

`⇔ x=1`

Vậy `S={1}`