Question

f(x)=2x2-5x+3
g(x)=4x2-12x+9
find: (f/g)(x)

Answer 1

f(x) = 2x^2 − 5x + 3 = (2x − 3)(x − 1)
g(x) = 4x^2 − 12x + 9 = (2x − 3)^2

So
(f/g)(x) = [ (2x − 3)(x − 1) ] / [ (2x − 3)^2 ] = (x − 1)/(2x − 3),

with domain restricted by g(x) ≠ 0, i.e. x ≠ 3/2. (The value x = 3/2 is a hole, not allowed.)