Multiply and divide rational expressions

Learning Objectives Factor complex polynomials in the numerator and denominator of rational expressions. Identify and state all non-permissible values (restrictions) for a given problem. Simplify a single rational expression by identifying and canceling common factors. Multiply two or more rational expressions and write the product in simplest form. Divide two rational expressions by multiplying by the reciprocal and simplifying the result. Solve multi-step problems involving both multiplication and division of rational expressions. Ever wondered how engineers simplify complex formulas for things like airflow over a wing or how economists model market behavior? They often use the same skills you're about to learn! ✈️ This tutorial will build upon your knowledge of fact...

TermDefinitionExample Rational ExpressionA fraction where both the numerator and the denominator are polynomials. The denominator cannot be the zero polynomial.(x^2 - 9) / (2x + 1) Non-Permissible Values (Restrictions)The values of a variable that would make the denominator of a rational expression equal to zero. Division by zero is undefined, so these values must be excluded from the domain.For the expression (x + 5) / (x - 3), the non-permissible value is x = 3, because it would make the denominator 3 - 3 = 0. We state this as x ≠ 3. FactoringThe process of breaking down a polynomial into a product of its factors (simpler polynomials). This is the most critical first step for simplifying.The polynomial x^2 - 5x + 6 can be factored into (x - 2)(x - 3). Simplest FormA rational expression...

Multiplication of Rational Expressions Given P, Q, R, S are polynomials: (P/Q) * (R/S) = (P * R) / (Q * S), where Q ≠ 0 and S ≠ 0. To multiply rational expressions, multiply the numerators together and multiply the denominators together. It is most efficient to factor everything first and cancel common factors before multiplying. Division of Rational Expressions Given P, Q, R, S are polynomials: (P/Q) ÷ (R/S) = (P/Q) * (S/R) = (P * S) / (Q * R), where Q ≠ 0, R ≠ 0, and S ≠ 0. To divide rational expressions, multiply the first expression by the reciprocal of the second expression. This is often called the 'Keep-Change-Flip' method.