At a certain temperature,$\operatorname{rod} A$ and $\operatorname{rod} B$ of different materials have lengths $L_A$ and $L_B$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $L_{A}: L_{B}$ is given by

• A
  $\frac{\alpha_A}{\alpha_B}$
• B
  $\frac{\alpha_B}{\alpha_A}$
• C
  $\frac{\alpha_A+\alpha_B}{\alpha_A}$
• D
  $\frac{\alpha_A+\alpha_B}{\alpha_B}$