Rewriting Rational Expressions Practice Test

Use polynomial division to write $$\frac{x^4+1}{x^2+1}$$ in the form $q(x)+\frac{r(x)}{x^2+1}$, where $\deg(r)<\deg(x^2+1)$.

Express $$\frac{2x^2+7x-3}{x+3}$$ as $q(x)+\frac{r(x)}{x+3}$ using the polynomial division algorithm, where $\deg(r)<\deg(x+3)$.