Solve R=frac{R_{1}R_{2}}{R_{1}+R_{2}}+R_{3}=1*2/1+2+3=

$$R = \frac { R _ { 1 } R _ { 2 } } { R _ { 1 } + R _ { 2 } } + R _ { 3 } = \frac { 1 \times 2 } { 1 + 2 } + 3 =$$

Evaluate (complex solution)

$$R=\frac{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}{R_{1}+R_{2}}\text{ and }\frac{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}{R_{1}+R_{2}}=\frac{11}{3}$$

Solve for R_3

$$R_{3}=\frac{11R_{2}+11R_{1}-3R_{1}R_{2}}{3\left(R_{1}+R_{2}\right)}$$

$$R=\frac{11}{3}\text{ and }R_{1}\neq -R_{2}$$

Solve for R_2

$$\left\{\begin{matrix}R_{2}=-\frac{R_{1}\left(3R_{3}-11\right)}{3R_{1}+3R_{3}-11}\text{, }&R_{1}\neq 0\text{ and }R=\frac{11}{3}\text{ and }R_{1}\neq \frac{11}{3}-R_{3}\\R_{2}\neq 0\text{, }&R=\frac{11}{3}\text{ and }R_{1}=0\text{ and }R_{3}=\frac{11}{3}\end{matrix}\right.$$