[tex] \dfrac{f(x+h)+f(x)}{h} [/tex]
Replace f(x) and f(x+h) by using the equation given for the problem.
[tex] =\dfrac{(2(x+h)^2-(x+h)-1)-(2x^2-x-1)}{h} [/tex]
Open all parenthesis
[tex]= \dfrac{2x^2+4xh+2h^2-x-h-1-2x^2+x+1}{h} [/tex]
Factor the h
[tex]= \dfrac{h(4x+2h-1)+2x^2-2x^2+1-1+x-x}{h} [/tex]
Other terms not in the parenthesis cancel each other out
[tex] \dfrac{h(4x+2h-1)}{h} [/tex]
Now, simplify
[tex]=4x+2h-1[/tex]
