Maclaurin series of fraction

Question

How to find $\frac{x+1}{x^2+x+1}$ maclaurin series.Tried splitting it into partial fractions but got stuck any hints?

Answer 1

Hint:$$\frac{x+1}{x^2+x+1}=\frac{(x+1)(x-1)}{(x^2+x+1)(x-1)}=\frac{x^2-1}{x^3-1}=\frac{1-x^2}{1-x^3}.$$