Lesson: February 3, 2025. Quiz: February 13, 2025.

  • Use the structure of rational expressions to rewrite simple rational expressions in different forms.
  • Understand that rational expressions form a system analogous to the system of rational numbers and use that understanding to multiply and divide rational expressions.

Assignment

There is not much here worth covering in notes.

  • If you are asked to simplify or rewrite a rational expression, factor it and divide out common factors between the numerator and denominator.
  • If you are asked to multiply expressions, remember that you multiply fractions straight across.
  • If asked to divide, remember that multiplying by the reciprocal is the same as dividing.

The one thing that absolutely must be pointed out is that your original domain applies to simplified expressions. The original expression is on the left and has a domain of $x\neq\left\{-9,0,8\right\}$.

\[\begin{align} \frac{x(x-8)(x+3)}{x(x-8)(x+9)} = \frac{x+3}{x+9} \end{align}\]

The simplified version on the right still has a domain of $x\neq\left\{-9,0,8\right\}$. The new version still has to follow the rules of the original, but the simplified version will be easier to work with.