Question

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

Answer 1

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

Ответ: 4.