Using the Maclaurin series for $\frac{1}{1-x}$, compute the Maclaurin series for: $$\frac{1+x}{1+x^2}$$.
What is the interval of convergence of this series?
Once you get the Maclaurin series for the function, I know how to find the convergence interval (I can use the Ratio test here, I believe) but how would I find the Maclaurin series for that using the one given?
$$\frac{1}{1-x}=\sum^\infty_{n=0}x^n$$