(a) Given polynomials \( p, q, r \), and \( s \) such that \( q \neq 0 \) and \( s \neq 0, \frac{p}{q} \cdot \frac{r}{s} \)

Did you know that polynomial fractions like \( \frac{p}{q} \cdot \frac{r}{s} \) follow the same multiplication rules as regular fractions? When you multiply them, you simply multiply the numerators together and the denominators together. So it becomes \( \frac{p \cdot r}{q \cdot s} \)! It’s a straightforward way to combine polynomial expressions and can come in handy for simplifying equations. One common mistake is forgetting to factor polynomials before multiplying or simplifying. Always try to factor \( p, q, r, \) and \( s \) when possible. This helps in seeing if any terms can cancel out, which can greatly simplify your final result and make it easier to handle in further calculations!