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**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)