Answer:
\(\boxed{\boxed{\dfrac{f(x)}{g(x)}=\dfrac{2x+3}{x+2}}}\)
Step-by-step explanation:
Here,
\(f(x)=2x^2-x-6\)
\(=2x^2-4x+3x-6\)
\(=2x(x-2)+3(x-2)\)
\(=(2x+3)(x-2)\)
And
\(g(x)=x^2-4\)
\(=x^2-2^2\)
\(=(x+2)(x-2)\)
Therefore,
\(\dfrac{f(x)}{g(x)}=\dfrac{(2x+3)(x-2)}{(x+2)(x-2)}\)
\(=\dfrac{2x+3}{x+2}\)
