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