Rationals Summary

Algebra 1 · Axiom Academy

SUMMARY Rational Expressions and Equations Algebraic fractions extend everything you know about numeric fractions — with one new demand: watch the domain at every step. Rational expressions are algebraic fractions. They obey the same rules as numeric fractions — factor, cancel common factors, and build a common denominator before adding. Domain restrictions are non-negotiable. Any value that makes a denominator zero is excluded — and the original restriction stays even after the expression simplifies. Factor before you operate. Whether you multiply, divide, add, or subtract, factoring first exposes the common factors and the LCD. Clearing denominators can manufacture extraneous solutions. Every solution must be checked in the original equation. The same machinery models the real world — work rates, travel rates, mixtures, and proportions are all rational-equation problems. Core Concept What a Rational Expression Is A rational expression is a fraction whose numerator and denominator are polynomials. It behaves like a numeric fraction: factor everything, then cancel common factors to put it in lowest terms. Simplify by: factoring numerator and denominator completely, then cancelling shared factors. The fraction parallel: just as reduces to , is reduced by factoring. Core Concept Domain Restrictions The denominator can never equal zero — division by zero is undefined. Set each denominator equal to zero and solve; those values are excluded from the domain.

This is the written version of the interactive lesson above. See the full Algebra 1 course.