Question

Vale 20 pontos
Qual a expressão mais simples equivalente a y-1/y+1 + y+1/y-1 - 4y/y^2-1

Answer 1

$\frac{y-1}{y+1}+ \frac{y+1}{y-1}- \frac{4y}{y^{2}-1}= \\ = \frac{(y-1)^{2}+ (y+1)^{2}-4y}{y^{2}-1}= \\ = \frac{y^{2}-2y+1+ y^{2}+2y+1-4y}{(y-1).(y+1)}}= \\ = \frac{2y^{2}-4y+2}{(y-1).(y+1)}= \\ = \frac{2(y^{2}-2y+1)}{(y-1).(y+1)}= \\ =\frac{2(y-1)^{2}}{(y-1).(y+1)}= \\ = \frac{2(y-1)}{y+1}$