(x+1)/9-(x-1)/6=2-(x+3)/2

(x+1)/9-(x-1)/6=2-(x+3)/2
(x+1)÷9-(x-1)÷6-2+(x+3)÷2=0
x+1/9-x-1/6-2+x+3/2=0
x+1/9-x-1/6+x+3/2-2=0
2(x+1)/2*9-3(x-1)/3*6+9(x+3)/9*2-2=0
2(x+1)-3(x-1)+9(x+3)/18-2=0
(2x+2)-(3x-3)+(9x+27)/18-2=0
2x+2-3x+3+9x+27/18-2=0
8x+32/18-2=0
8x+32/18-18*2/18=0
(8x+32)-18*2/18=0
(8x+32)-36/18=0
8x+32-36/18=0
8x-4/18=0
4(2x-1)/18=0
2(2x-1)/9=0
2x-1=0
2x=1
x=1÷2
x=1/2