CMOQR 2019 Problem 1

A function $f$ is called injective if when $f(n) = f(m)$ , then $n = m$ . Suppose that $f$ is injective and $\frac{1}{f(n)}+\frac{1}{f(m)}=\frac{4}{f(n) + f(m)}$ . Prove $m = n$