solve for "R" (difficult)

R/(R+1)  + 2 =  3R / (R+2)   subtract the fraction on the left side from both sides

2 = 3R/(R + 2) - R/(R + 1)      get a common denominator on the right side

2 = [3R(R+1) - R(R + 2)]/ [(R + 2)(R + 1)]    cross- multiply

2 [(R + 2)(R + 1)] = [3R(R+1) - R(R + 2)]  simplify

2R^2 + 6R + 4 = 3R^2 + 3R - R^2 - 2R

2R^2 + 6R + 4 = 2R^2 + R        subtract 3R^2 + R from both sides

5R + 4 = 0             subtract 4 from both sides

5R = -4                  divide both sides by 5

R= -4/5