How can I simplify [math]\frac{1}{1+x^{m-n}}+ \frac{1}{1+x^{n-m}}?[/math]
How can I prove that for all positive reals [math]x_1, \ldots, x_n[/math] with [math]x_1 x_2 \ldots x_n=1[/math] we have [math]\frac{1}{n-1+x_1}+\ldots+\frac{1}{n-1+x_n} \le 1 [/math]?