Originally Posted by
Caddym89 Hi guys, this is part of the harder portion of my homework, and I'm struggling to know where to start. Could someone point me in the right direction? Thanks a lot.
a) In this exercise, we find the range (i.e. the possible values) of (6x + 5) / (3x^{2 }+ 4x + 2)
Let D = (6x + 5) / (3x^{2 }+ 4x + 2) for all x.
i) Show that 3Dx^{2} + (4D - 6)x + 2D - 5 = 0
ii) Hence, show that 3Dx2 + (4D - 6)x + 2D - 5 = 0 has real solutions in x if and only if (D - 3)(2D + 3) <= 0
iii) Hence, find the range of (6x + 5) / (3x^{2} + 4x + 2)
b) Find the range of (x^{2 }- 6x + 5) / (x^{2} + 2x + 1)