BALTIC-WAY 2003 Problem 1

Let $\mathbb{Q}_{+}$be the set of positive rational numbers. Find all functions $f: \mathbb{Q}_{+} \rightarrow \mathbb{Q}_{+}$which for all $x \in \mathbb{Q}_{+}$fulfil

(1) $f\left(\frac{1}{x}\right)=f(x)$

(2) $\left(1+\frac{1}{x}\right) f(x)=f(x+1)$