Question

(objetivo) x-1/x-2 - x-2/x-1 = 8/3?

Answer 1

$\frac{x-1}{x-2}-\frac{x-2}{x-1}=\frac{8}{3}\\ \\ \frac{(x-1)^2-(x-2)^2}{(x-1)(x-2)}=\frac{8}{3}\\ \\ \frac{x^2-2x+1-(x^2-4x+4)}{x^2-2x-x+2}=\frac{8}{3}\\ \\ \frac{x^2-2x+1-x^2+4x-4}{x^2-2x-x+2}=\frac{8}{3}\\ \\ \frac{2x-3}{x^2-3x+2}=\frac{8}{3}\\ \\ 8x^2-24x+16=6x-9\\ \\ 8x^2-24x-6x+16+9=0\\ \\ \boxed{8x^2-30x+25=0}$

Daqui prá frente é com vc. (Bháskara)