Two uniform metal rods of lengths $ {{l}_{1}} $ and $ {{l}_{2}} $ and linear coefficients of expansion $ {{\alpha }_{1}} $ and $ {{\alpha }_{2}} $ respectively are connected to form a single rod of length $ ({{l}_{1}}+{{l}_{2}}). $ When the temperature of the combined rod is raised by t ?C, the length of each rod increases by the same amount. Then $ \left( \frac{{{\alpha }_{2}}}{{{\alpha }_{1}}+{{\alpha }_{2}}} \right) $ is: