1/(x-5)-1/(x-7)=1/(x-1)-1/(x-3)

$\frac{1}{(x-5)}^{(x-7}-\frac{1}{(x-7)}^{(x-5}=\frac{1}{(x-1)}^{(x-3}-\frac{1}{(x-3)}^{(x-1}\\\frac{x-7-x+5}{(x-5)(x-7)}=\frac{x-3-x+1}{(x-1)(x-3)} \\\frac{-2}{(x-5)(x-7)}^{((x-1)(x-3)}-\frac{-2}{(x-1)(x-3)}^{((x-5)(x-7)}=0\\\frac{-2(x^2-4x+3)+2(x^2-12x+35)}{(x-1)(x-3)(x-5)(x-7)}=0\\\frac{-2x^2+8x-6+2x^2-24x+70}{(x-1)(x-3)(x-5)(x-7)}=0\\\frac{-16x+64}{(x-1)(x-3)(x-5)(x-7)}=0\\\frac{-16(x-4)}{(x-1)(x-3)(x-5)(x-7)}=0\\x=4$

Ответ: 4.