$\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_1+R_2}=\frac{R_2(R_1+R_2)+R_1(R_1+R_2)+R_1{R}_2}{R_1{R}_2(R_1+R_2)}=\frac{3R_1{R}_2+R_r^2+R_1^2}{R_1{R}_2(R_1+R_2)}\backslash frac\{1\}\{R\_1\}+\backslash frac\{1\}\{R\_2\}+\backslash frac\{1\}\{R\_1+R\_2\}\backslash \; =\backslash frac\{R\_2\backslash left(R\_1+R\_2\backslash right)+R\_1\backslash left(R\_1+R\_2\backslash right)+R\_1R\_2\}\{R\_1R\_2\backslash left(R\_1+R\_2\backslash right)\}=\backslash frac\{3R\_1R\_2+R\_r^2+R\_1^2\}\{R\_1R\_2\backslash left(R\_1+R\_2\backslash right)\}$