lean_workbook_plus_75694

Find all functions $f: \mathbb{Q}^{+}\to \mathbb{R}$ such that $f\left(x\right)=f\left(\frac{1}{x}\right)$ and $xf\left(x\right)=\left(x+1\right)f\left(x-1\right)$ for all positive rational numbers $x$ and $f\left(1\right)=1$ .