Rational Expressions and Equations

SAT Math · Axiom Academy

Rational Expressions & Equations Simplify, Add, and Solve Rational Expressions What is a Rational Expression? A rational expression is a fraction where the numerator and/or denominator contain variables. The denominator can NEVER equal zero. We must identify and state restrictions before simplifying. Simplifying Rational Expressions Cancel common factors in the numerator and denominator. (NOT terms—only factors!) You can only cancel factors, not terms. Correct Approach: Factor First State restrictions from denominator Note: Even after simplification, still cannot be used! Adding & Subtracting Rational Expressions Key Rule: Find the Least Common Denominator (LCD) An equation with rational expressions on one or both sides. Find restrictions (values that make any denominator 0) Simplify and solve the resulting equation Check: Make sure solutions don't violate restrictions A solution that makes any denominator zero is called an extraneous solution and must be rejected.

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