Maths

Let y = f(x)/g(x) = (x^2 + 2x - 2) / (-2x^2 - 12x - 23)
y(-2x^2 - 12x - 23) = x^2 + 2x - 2
(1 + 2y)x^2 + (2 + 12y)x + (23y - 2) = 0
For real x, discriminant >= 0
(2 + 12y)^2 - 4(1 + 2y)(23y - 2) >= 0
4 + 48y + 144y^2 - 4(46y^2 + 19y - 2) >= 0
4 + 48y + 144y^2 - 184y^2 - 76y + 8 >= 0
-40y^2 - 28y + 12 >= 0
10y^2 + 7y - 3 <= 0
(10y - 3)(y + 1) <= 0
-1 <= y <= 0.3
The greatest value is 0.3, the smallest value is -1