BG-MO 1977 Problem 1

For natural number $n$ and real numbers $\alpha$ and $x$ satisfy the inequalities $\alpha^{n+1}\le x\le1$ and $0<\alpha<1$ . Prove that $$\prod_{k=1}^n\left|\frac{x-\alpha^k}{x+\alpha^k}\right|\le\prod_{k=1}^n\left|\frac{1-\alpha^k}{1+\alpha^k}\right|.$$ Borislav Boyanov