Simplify the difference quotient $\frac{f\left(x\right)-f\left(a\right)}{x-a}$ for the function $f\left(x\right)=2x^3-\frac{1}{x}$.

$\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2ax(x^3-3a^{2}x-3a{x}^2+a^3)+1}{ax}$

$\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2ax(x^3+3a^{2}x+3a{x}^2+a^3)+1}{ax}$

$\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2ax(x^2+x+a^2)+1}{ax}$

$\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2ax(x^2+ax+a^2)+1}{ax}$