Question

If f(x)=2x^2-x-6 and g(x)=x^2-4 find f(x)/g(x)

Answer 1

$\dfrac{f(x)}{g(x)}=\dfrac{2x^2-x-6}{x^2-4}\\ \dfrac{f(x)}{g(x)}=\dfrac{2x^2-4x+3x-6}{(x-2)(x+2)}\\ \dfrac{f(x)}{g(x)}=\dfrac{2x(x-2)+3(x-2)}{(x-2)(x+2)}\\ \dfrac{f(x)}{g(x)}=\dfrac{(2x+3)(x-2)}{(x-2)(x+2)}\\ \dfrac{f(x)}{g(x)}=\dfrac{2x+3}{x+2}$