Question

Resolver, em R, a equaçao

$\frac{x-1}{x-2}- \frac{x-2}{x-1}= \frac{8}{3}$

Answer 1

$\frac{x-1}{x-2}-\frac{x-2}{x-1}=\frac{8}{3}\\ \\ \boxed{Veja \ que \ \frac{a}{b}-\frac{b}{a}=\frac{a^2-b^2}{ab}}\\ \\ Assim:\\ \\ \frac{x-1}{x-2}-\frac{x-2}{x-1}=\frac{(x-1)^2-(x-2)^2}{(x-2)(x-1)}=\frac{8}{3}\\ \\ \frac{x^2-2x+1-(x^2-4x+4)}{x^2-3 x+2}=\frac{8}{3}\\ \\ \frac{2x-3}{x^2-3x+2}=\frac{8}{3}\\ \\ 8x^2-24x+16=6x-9\\ \\ 8x^2-30x+25=0\\ \\ S=\{\frac{5}{4},\frac{5}{2}\}$