Question

If f(x) = 2x2 - x - 6 and g(x) = x2 - 4, find f(x) ÷ g(x).

Answer 1

$f(x)=2x^2-x-6,\ g(x)=x^2-4\\\\f(x)\div g(x)=\dfrac{f(x)}{g(x)}=\dfrac{2x^2-x-6}{x^2-4}=\dfrac{2x^2-4x+3x-6}{x^2-2^2}\\\\=\dfrac{2x(x-2)+3(x-2)}{(x-2)(x+2)}=\dfrac{(x-2)(2x+3)}{(x-2)(x+2)}=\dfrac{2x+3}{x+2}\ for\ x\neq0\\\\Answer:\ f(x)\div g(x)=\dfrac{2x+3}{x+2}$

$Used:\ a^2-b^2=(a-b)(a+b)$