# Multiplication and Division of Rational Expressions

In this section Sal encourages you to pause the videos, to think about restrictions needed for expressions to really be equivalent.  Do it!

1. $\rhd$ Monomials (5:55)  This video uses function notation $f(x)$ and analyzes the expressions as functions.  –[Example 1] $\frac{6x^3}{5} \cdot \frac{2}{3x}$  — [Example 2] $\frac{2x^4}{7} \div \frac{5x^4}{4}$
2. $\star$ (basic)  Multipy and divide rational expressions   Multiply the following monomials and determined if the result is defined when $b = 0$ $\frac{-5b^3}{6} \cdot \frac{3b^2}{-10}$ .
3. $\rhd$ Multiply rational expressions (4:51) $\frac{a^2 - 4}{a^2 - 1} \cdot \frac{a - 2}{a - 1}$  noting that $a \neq -2$ and $a \neq -1$.
4. $\rhd$ Dividing rational expressions (4:09) $\frac{2p+6}{p+5} \div \frac{10}{4p+20} = \frac{5(p+3)}{4}$ where $p \neq -5$.
5. $\star$ Multiplying rational expression practice $\frac{4z^2 +24z}{3z^2 - 9z -12} \cdot \frac{z^2 - 4z -5}{z-4}$
6. $\rhd$ Mulitply and expressing as a simplified rational expression.  State the domain. (3:37) $\frac{3x^2y}{2ab}\frac{14a^2b}{18xy^2} = \frac{7ax}{6y}.$  Note that $a, b, x, y \neq 0$.
7. $\star$ Divide the rational expressions and simplify $\frac{10n^2 + 23n - 5}{4n^2 + 6n} \div \frac{25n^2 - 10n +1}{7n+3}$