Two rods joined end to end expand by the same amount: ratio involving their lengths

1. A.
   $\frac{\alpha_2}{\alpha_1}$
2. B.
   $\frac{\alpha_1}{\alpha_2}$
3. C.
   $\frac{\alpha_2}{\alpha_1+\alpha_2}$
4. D.
   $\frac{\alpha_1}{\alpha_1-\alpha_2}$

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1. A.
   $\frac{\alpha_i}{\alpha_c+\alpha_i}$
2. B.
   $\frac{\alpha_c}{\alpha_c+\alpha_i}$
3. C.
   $\frac{\alpha_i-\alpha_c}{\alpha_c+\alpha_i}$
4. D.
   $\frac{\alpha_c-\alpha_i}{\alpha_c+\alpha_i}$

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