my answer is c < = 3. dunno if my method is correct
y = (x^2 + 2x - c) / (x - 1)
y (x - 1 ) = x^2 + 2x - c
yx - y = x^2 + 2x - c
x^2 + 2x - yx - c + y = 0
x^2 + (2 - y) x + (y - c) = 0
Since x is real, discriminant > = 0
(2 - y)^2 - 4 (1) (y - c) > = 0
4 - 4y + y^2 - 4y + 4c > = 0
y^2 - 8y + (4c + 4) > = 0
Since the equation needs
to be >=0, it means it has either equal roots or no real
roots
so (-8)^2 - 4 (1) (4c + 4) < = 0
64 - 16c - 16 <
= 0
48 - 16c <
= 0
48 <
= 16c
c >
= 3
I was waiting for someone to answer :)
Almost correct
Editing in red
Give me a while to post a graph for further explanations
