Two rods,one of copper $(Cu)$ and the other of iron $(Fe)$,having initial lengths $L_1$ and $L_2$ respectively,are connected together to form a single rod of length $L_1+L_2$. The coefficients of linear expansion of $Cu$ and $Fe$ are $\alpha_c$ and $\alpha_i$ respectively. If the length of each rod increases by the same amount when their temperatures are raised by $t^{\circ}C$,then the ratio $\frac{L_1-L_2}{L_1+L_2}$ will be:

• A
  $\frac{\alpha_i}{\alpha_c+\alpha_i}$
• B
  $\frac{\alpha_c}{\alpha_c+\alpha_i}$
• C
  $\frac{\alpha_i-\alpha_c}{\alpha_c+\alpha_i}$
• D
  $\frac{\alpha_c-\alpha_i}{\alpha_c+\alpha_i}$