Question

(EPCAR) O valor da expressão:

$(\frac{x { }^{ - 2 } - y {}^{ - 2} }{x {}^{ - 1} + y {}^{ - 1} }) \times ( \frac{x {}^{2}y + xy {}^{2} }{x {}^{2} - y {}^{2}})$
Em que x, y pertencem a R e x≠y e x≠-y é:

a) -1
b) -2
c) 1
d) 2
​

Answer 1

$(\frac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}).(\frac{x.y.(x+y)}{(x+y).(x-y)})\\\\(\frac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}).(\frac{x.y}{x-y})\\(\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x}+\frac{1}{y}}).(\frac{x.y}{x-y})\\\\(\frac{\frac{y^2-x^2}{(x.y)^2}}{\frac{y+x}{x.y}}).(\frac{x.y}{x-y})\\\\([\frac{y^2-x^2}{(x.y)^2}].[\frac{x.y}{y+x}]).(\frac{x.y}{x-y})\\\\(\frac{y^2-x^2}{(x.y).(y+x)}).(\frac{x.y}{x-y})\\\\\frac{y^2-x^2}{(y+x).(x-y)}\\\\\frac{(y+x).(y-x)}{(x+y).(x-y)}\\\\\frac{y-x}{x-y}\\\\\frac{-(x-y)}{(x-y)}\\\\-1$

a) -1

Dúvidas só perguntar!