F(x)= 2x^2-3x-9 G(x)= 4x^2-9 find (f/g) (x)

This is about division of polynomials.

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

f(x) = 2x² - 3x - 9

g(x) = 4x² - 9

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)

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)

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