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Rational Expressions and Equations

Chapter 6. Rational Expressions and Equations. 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

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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. Addition and Subtraction of Rational Expressions § 6.2

  4. Add and Subtract Expressions with a Common Denominator To Add or Subtract Rational Expressions with a Common Denominator To add or subtract rational expressions, use the following rules. ADDITION SUBTRACTION To add or subtract rational expressions with a common denominator, Add or subtract the expressions using the rules given above. Simplify the expression if possible.

  5. Example

  6. Find the Least Common Denominator (LCD) To Find the Least Common Denominator (LCD) of Rational Expressions Write each nonprime coefficient (other than 1) of monomials that appear in denominators as a product of prime numbers. Factor each denominator completely. Any factors that occur more than once should be expressed as powers. For example, (x + 5)(x + 5) should be expressed as (x + 5)2. List all different factors (other than 1) that appear in any of the denominators. When the same factor appears in more than one denominator, write the factor with the highest power that appears. The least common denominator is the product of all the factors found in step 3.

  7. Find the Least Common Denominator (LCD) Example Find the LCD of the expression. Factor both denominators. The factors are 2, x, and x – 2. Multiply the factors raised to the highest power that appears for each factor.

  8. Unlike Denominators To Add or Subtract Rational Expressions with Different Denominators Determine the least common denominator (LCD). Rewrite each fraction as an equivalent fraction with the LCD. This is done by multiplying both the numerator and denominator of each fraction by any factors needed to obtain the LCD. Leave the denominator in factored form, but multiply out the numerator. Add or subtract the numerators while maintaining the LCD. When it is possible to reduce the fraction by factoring the numerator, do so.

  9. Unlike Denominators Example Add First determine the LCD. The LCD = xy. Now write each fraction with the LCD. Do this by multiplying both numerator and denominator of each fraction by any factors needed to obtain the LCD. continued

  10. Unlike Denominators Now, add the numerators while maintaining the LCD.

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