1/2=1/1r+1/2r+1/3r r=??????

\(\dfrac{1}{2} = \dfrac{1}{1}r+\dfrac{1}{2}r+\dfrac{1}{3}r\\ 3 = 6r + 3r + 2r\\ 11r = 3\\ r = \dfrac{11}{3}\)

Or you mean

\(\dfrac{1}{2}=\dfrac{1}{1r}+\dfrac{1}{2r}+\dfrac{1}{3r}\\ \dfrac{r}{2} = 1+\dfrac{1}{2}+\dfrac{1}{3} =\dfrac{11}{6}\\ 3r = 11\\ r=\dfrac{11}{3}\)

The answers are the same, never mind

MAX:

 

The answer should be the reverse of what you got:

r =3/11