The Lucas numbers are defined by $$L_0 = 1, L_1=3$$ $$L_n = L_{n-2} + L_{n-1}$$

I used this knowledge to get an equation for the nth Lucas number as follows: $$L(x) = \frac{1+2x}{1-x-x^2}$$

Now I am asked to find a closed formula for this equation and was wondering how I would make this equation be in closed form.