Periodic functions/Rational ratio of lengths/Sum periodic/Exercise

Let

$f_{1},f_{2}\colon \mathbb {R} \longrightarrow \mathbb {R}$

be periodic functions with periods respectively ${}L_{1}$ and ${}L_{2}$. The quotient ${}L_{1}/L_{2}$ is a rational number. Prove that ${}f_{1}+f_{2}$ is also a periodic function.

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