Math 101 Intermediate Algebra    Multiplication and Division of Rational Expressions Chapter 7, Section 1 Reducing Rational Expressions to Lowest Terms A rational expression is reduced to lowest terms when the numerator and denominator have no common factors other than 1. To simplify a rational expression means to reduce the rational expression to lowest terms. To reduce rational expressions to lowest terms..... Factor both the numerator and denominator as completely as possible. Cancel factors common to both the numerator and denominator. Multiplying Rational Expressions For a, b, c, and d expressions with b 0 and d 0: To multiply rational expressions..... Factor all numerators and denominators as far as possible. Cancel any common factors. Multiply the numerators. Multiply the denominators. Reduce the answer when possible. Dividing Rational Expressions For a, b, c, and d expressions with b 0, c 0, and d 0:  To multiply rational expressions..... Invert the divisor (the second or bottom fraction). Multiply the resulting rational expressions.