Answer: OPTION C.
Step-by-step explanation:
Given the functions:
[tex]f(x)=2x^2-x-6\\\\g(x)=x^2-4[/tex]
We need to divide f(x) by g(x) in order to find [tex]f(x)[/tex]÷[tex]g(x)[/tex]. Then:
[tex]f(x)[/tex]÷[tex]g(x)[/tex][tex]=\frac{2x^2-x-6}{x^2-4}[/tex]
Factorizing and simplifying, we get:
[tex]f(x)[/tex]÷[tex]g(x)[/tex][tex]=\frac{(2x+3)(x-2)}{(x+2)(x-2)}[/tex]
[tex]f(x)[/tex]÷[tex]g(x)[/tex][tex]=\frac{2x+3}{x+2}[/tex]
