Question

A expressão algébrica (1/x+1 + 1/1-x) ( x²-1) é equivalente a:
a) -2
b) -x
c) 2x
d) x
e) 2

Answer 1

[1/(x+1) + 1/(1-x)].(x²-1) = 
mmc (x+1) e (1-x) = (x+1).(1-x)
(x+1).(1-x):(x+1).1 = 1-x
(x+1).(1-x): (1-x) = x+1
[(x+1)+(1-x)]/(x+1).(1-x) . (x+1).(x-1) = 
[(x+1)+(1-x)]/(1-x) . -(1-x) = 
[(x+1)+(1-x)]/(-1) = 
(x+1+1-x)/(-1) = 
2/-1 = -2