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
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