Respuesta :

This is about division of polynomials.

(f/g)(x) = (x + 1)/(2x + 3)

  • (f/g) (x) simply means we divide f(x) by g(x)

  • We are given;

f(x) = 2x² - 3x - 9

g(x) = 4x² - 9

  • To divide this, let's simplify each function to its factors using the sun-product pattern.

f(x) = 2x² - 3x + 6x - 9

Let's collect like terms;

f(x) = x(2x - 3) + 1(2x - 3)

Rewriting in factored form gives;

f(x) = (x + 1)(2x - 3)

  • Similarly;

g(x) = 4x² - 9

g(x) = 4x² + 6x - 6x - 9

g(x) = 2x(2x + 3) - 3(2x + 3)

Rewriting in factored form gives;

g(x) = (2x + 3)(2x - 3)

Thus;

(f/g)(x) = ((x + 1)(2x - 3))/((2x + 3)(2x - 3))

(f/g)(x) = (x + 1)/(2x + 3)

Read more at;

brainly.in/question/37643694

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