Euclid for polynomials

Euclid for polynomials

I have a question bout euclid polynomials.
If $C(x) =x^4−1$ and $D(x) =x^3+x^2
How do I find a polynomials $A(x)$ and $B(x)$ such that $A(x)C(x)
+B(x)D(x) =x+1$ for all $x$?