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}