Mathematics » Rational Expressions and Equations » Add and Subtract Rational Expressions with a Common Denominator

Add and Subtract Rational Expressions Summary I

Key Concepts

  • Rational Expression Addition
    • If \(p,q,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r\) are polynomials where \(r\ne 0\), then
      \(\frac{p}{r}+\frac{q}{r}=\frac{p+q}{r}\)

    • To add rational expressions with a common denominator, add the numerators and place the sum over the common denominator.
  • Rational Expression Subtraction
    • If \(p,q,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}r\) are polynomials where \(r\ne 0\), then
      \(\frac{p}{r}-\frac{q}{r}=\frac{p-q}{r}\)

    • To subtract rational expressions, subtract the numerators and place the difference over the common denominator.

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