ZA-SAMO 2009 Problem 4

Let $x_1,x_2,\dots,x_n$ be a finite sequence of real numbersm mwhere $0<x_i<1$ for all $i=1,2,\dots,n$ . Put $P=x_1x_2\cdots x_n$ , $S=x_1+x_2+\cdots+x_n$ and $T=\frac{1}{x_1}+\frac{1}{x_2}+\cdots+\frac{1}{x_n}$ . Prove that $$\frac{T-S}{1-P}>2.$$