Given that the domain of F (x) and G (x) is r, where f (x) is odd, G (x) is even, and f (x) + G (x) = 1 / (square of X + X + 1), then the range of F (x) / G (x) is? Why?

Given that the domain of F (x) and G (x) is r, where f (x) is odd, G (x) is even, and f (x) + G (x) = 1 / (square of X + X + 1), then the range of F (x) / G (x) is? Why?

F (x) is an odd function, G (x) is an even function, f (x) + G (x) = 1 / (x ^ 2 + X + 1), then f (- x) + G (- x) = g (x) - f (x) = 1 / (x ^ 2-x + 1) add 2g (x) = 2 (x ^ 2 + 1) / (x ^ 2-x + 1) (x ^ 2 + X + 1) subtract 2F (x) = - 2x / (x ^ 2-x + 1) (x ^ 2 + X + 1) so f (x) / g (x) = - X / (x ^ 2 + 1) let a = - X / (x ^ 2 + 1) ax ^ 2 + X + a = 0