Mathematics » Rational Expressions and Equations » Simplify Rational Expressions

Simplifying Rational Expressions Summary

Key Concepts

  • Determine the Values for Which a Rational Expression is Undefined
    1. Set the denominator equal to zero.
    2. Solve the equation, if possible.
  • Simplified Rational Expression
    • A rational expression is considered simplified if there are no common factors in its numerator and denominator.
  • Simplify a Rational Expression
    1. Factor the numerator and denominator completely.
    2. Simplify by dividing out common factors.
  • Opposites in a Rational Expression
    • The opposite of \(a-b\) is \(b-a\).
      \(\begin{array}{cccccc}\frac{a-b}{b-a}=-1\hfill & & & & & a\ne 0,b\ne 0,\text{a}\ne \text{b}\hfill \end{array}\)

Glossary

rational expression

A rational expression is an expression of the form \(\frac{p}{q}\), where p and q are polynomials and \(q\ne 0.\)

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