Find (f/g)(x)

Question

F(x)=2x^2-5x+3

 

G(x)=4x^2-12x+9

 

Find (f/g)(x)

Answer 1

f(x) = 2x² - 5x + 3 = (2x - 3)(x - 1)
g(x)= 4x²-12x+9 = (2x - 3)²

 

(f/g)(x) = f(x)/g(x)

            = (2x - 3)(x - 1)/(2x - 3)²

            = (x - 1)/(2x -3)

 

This is true for x except x = 3/2, since the denominator cannot be 0.