x+1/(x*2+2)+(x*2-x+2)/(3x+2)=13/6
x+1/(2*(x+1))+(x+2)/(3x+2)=13/6
1/2+(x+2)/(3x+2)=13/6
(x+2)/(3x+2)=13/6-1/2=(13-3)/6=10/6=5/3
(x+2)/(3x+2)=5/3
3(x+2)=5(3x+2)
3x+6=15x+10
12x=-4
x=-1/3
x+1/(x*2+2)+(x*2-x+2)/(3x+2)=13/6
x+1/(2*(x+1))+(x+2)/(3x+2)=13/6
1/2+(x+2)/(3x+2)=13/6
(x+2)/(3x+2)=13/6-1/2=(13-3)/6=10/6=5/3
(x+2)/(3x+2)=5/3
3(x+2)=5(3x+2)
3x+6=15x+10
12x=-4
x=-1/3