Division of Algebraic Fractions (Rational Expressions)
Big Idea: Dividing algebraic fractions follows the same principle as dividing numerical fractions — multiply by the reciprocal — but now we work with variables, factoring, and cancellation of algebraic expressions.
1. Quick Review: Dividing Numerical Fractions
Recall that dividing by a fraction means multiplying by its reciprocal (flipping the second fraction):
$$ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} $$
For example: $ \frac{2}{3} \div \frac{5}{7} = \frac{2}{3} \times \frac{7}{5} = \frac{14}{15} $