Are you perhaps trying to solve it for v2?

\(\displaystyle V_{ave} = \frac{2 v_1 v_2}{v_1 + v_2}\)

\(\displaystyle (v_1 + v_2) V_{ave} = 2 v_1 v_2\)

\(\displaystyle v_1 V_{ave} + v_2 V_{ave} = 2 v_1 v_2\)

\(\displaystyle v_2 V_{ave} - 2v_1 v_2 = - v_1 V_{ave}\)

\(\displaystyle v_2 ( V_{ave} - 2 v_1 ) = - v_1 V_{ave}\)

\(\displaystyle v_2 = \frac{- v_1 V_{ave} }{ V_{ave} - 2 v_1}\)

or

\(\displaystyle v_2 = \frac{v_1 V_{ave} }{ 2 v_1 - V_{ave}}\)

-Dan