function question

Question

Let f, g, and h be three functions defined as

F(x)=7x^2-3x+2

G(x)=-3x^2-12x+7

H(x)=4x^2+21x-18

Find, and if possible, simplify

[f+g/h](x)

Answer 1

The functions are f(x) = 7x² - 3x + 2, g(x) = - 3x² - 12x +7 and h(x) = 4x² + 21x - 18.

[(f + g)/h](x) = [f(x) + g(x)] / h(x)

                   = [(7x² - 3x + 2) + (- 3x² - 12x +7)] / (4x² + 21x - 18)

                   = [(7x² - 3x²) + (- 3x - 12x) + (2 + 7)] / (4x² + 21x - 18)

                   = (4x² - 15x + 9) / (4x² + 21x - 18)

                   = (4x² - 12x - 3x + 9) / (4x² + 24x - 3x - 18)

                   = [4x(x - 3) - 3(x - 3)] / [4x(x + 6) - 3(x + 6)]

                   = [(4x - 3)(x - 3)] / [(4x - 3)(x + 6)]

                   = (x - 3) / (x + 6).