Two rods,one of aluminum and another of steel,have initial lengths $l_1$ and $l_2$ respectively. They are joined together to form a single rod of length $(l_1 + l_2)$. If the coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively,and the increase in length for both rods is the same when the temperature of both is increased by $t \ ^\circ C$,then $\frac{l_1}{l_1 + l_2} = \dots$

• A
  $\frac{\alpha_s}{\alpha_a}$
• B
  $\frac{\alpha_a}{\alpha_s}$
• C
  $\frac{\alpha_s}{(\alpha_a + \alpha_s)}$
• D
  $\frac{\alpha_a}{(\alpha_a + \alpha_s)}$