Question

Sabe-se que A= -x/1-x +1 e B= -1 -x/x-1. se você simplificar a fração A/B, que valor você vai obter?
 

Answer 1

$A=\dfrac{-x}{1-x}+1=\dfrac{-x+1-x}{1-x}=\dfrac{-2x+1}{1-x}\cdot\dfrac{(-1)}{(-1)}=\dfrac{2x-1}{x-1}$.

$B=-1-\dfrac{x}{x-1}=\dfrac{-x+1-x}{x-1}=\dfrac{-2x+1}{x-1}=\dfrac{-(2x-1)}{x-1}$

Logo:

$\dfrac{A}{B}=\dfrac{\dfrac{2x-1}{x-1}}{\dfrac{-(2x-1)}{x-1}}=\dfrac{2x-1}{x-1}\cdot\dfrac{x-1}{-(2x-1)}=\dfrac{2x-1}{-(2x-1)}=-1$

Alternativa B