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Rational Expressions and Equations

Learn about the domains of rational functions, multiplication and division of rational expressions, simplifying rational expressions, and solving rational equations.

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Rational Expressions and Equations

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  1. Chapter 6 Rational Expressions and Equations

  2. Chapter Sections 6.1 – The Domains of Rational Functions and Multiplication and Division of Rational Expressions 6.2 – Addition and Subtraction of Rational Expressions 6.3 – Complex Fractions 6.4 – Solving Rational Equations 6.5 – Rational Equations: Applications and Problem Solving 6.6 – Variation

  3. The Domains of Rational Functions and Multiplication and Division of Rational Expressions § 6.1

  4. Find the Domains of Rational Functions A rationalexpressionis an expression of the form where p and q are polynomials and q  0. Examples: Note that the denominator of a rational expression cannot equal 0 because the fraction bar is a division symbol and division by 0 is undefined.

  5. Find the Domains of Rational Functions Rational Function A rational function is a function of the form y = f(x) = p/q where p and q are polynomials and q ≠ 0. Examples:

  6. Find the Domains of Rational Functions Domain of a Rational Function A domain of a rational function y = f(x) = p/q is the set of all real numbers for which the denominator, q, is not equal to 0. Examples:

  7. Find the Domains of Rational Functions Example Determine the domain of

  8. sign of the numerator a - a - a a sign of the fraction + - + b b b -b sign of the denominator = = Signs of a Fraction Three signsare associated with any fraction: the sign of the numerator, the sign of the denominator, and the sign of the fraction. Changing any two of the three signs of a fraction does not change the value of the fraction

  9. Simplify Rational Expressions A rational expression is simplifiedwhen the numerator and denominator have no common factors other than 1. Example The fraction 6/9 is not simplified because the 6 and 9 both contain the common factor 3. When the 3 is factored out, the simplified fraction is 2/3.

  10. Simplify Rational Expressions • Factor both the numerator and denominator as completely as possible. • Divide both the numerator and denominator by any common factors. Simplify

  11. Multiply Rational Expressions To Multiply Rational Expressions To multiply rational expressions, use the following rule: To multiply rational expressions, follow these steps. Factor all numerators and denominators as far as possible. Divide out any common factors Multiply using the above rule Simplify the answer when possible.

  12. Multiply Rational Expressions Example Multiply.

  13. Divide Rational Expressions To Divide Rational Expressions To divide rational expressions, use the following rule: To divide rational expressions, multiply the first rational expression by the reciprocal of the second rational expression.

  14. Divide Rational Expressions Example Divide

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