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Chapter 8 Rational Expressions

8.1 Simplifying Rational Expressions 8.2 Multiplying and Dividing Rational Expressions 8.3 Finding the Least Common Denominator 8.4Adding and Subtracting Rational Expressions Putting It All Together 8.5Simplifying Complex Fractions 8.6Solving Rational Equations 8.7Applications of Rational Equations 8 Rational Expressions

Adding and Subtracting Rational Expressions8.4 Add or Subtract Rational Expressions with a Common Denominator In order to add or subtract fractions, they must have a common denominator. In the same way rational expressions must have common denominators in order to be added or subtracted. Example 1 a)Since the fractions have the same denominator, subtract the terms in the numerator and keep the common denominator. Solution b) Since the fractions have the same denominator, subtract the terms in the numerator and keep the common denominator. Subtract terms in numerator. Add terms in numerator. Combine like terms

We can generalize the procedure for adding and subtracting rational expressions that have a common denominator as follows. All answers to a sum or difference of rational expressions should be in lowest terms. If necessary simplify the result to lowest terms by factoring the numerator and dividing the numerator and denominator by the greatest common factor. Example 2 Solution Add terms in numerator. Reduce to lowest terms.

Example 3 Solution Subtract terms in numerator. Reduce to lowest terms. Distribute negative into parenthesis. Combine like terms. Factor the numerator.

Add or Subtract Rational Expressions with a Different Denominators To add or subtract rational expressions with different denominators we must begin by rewriting each expression with the least common denominator. Then we can add or subtract and simplify the result. Let’s try a few examples.

Example 4 Solution Write each expression with the LCD. Step 1&2: Factor denominators and write down the LCD. Step 3: Rewrite each rational expression as an equivalent rational expression with the LCD. Step 4: Add numerators and keep the common denominator in factored form. Add numerators. Distribute. Combine like terms. Reduce. 6 Factor.

Example 5 Solution Write each expression with the LCD. Subtract numerators.

Example 6 Solution Write each expression with the LCD. Add numerators. Distribute. Combine like terms. Factor. Reduce.

Example 7 Solution Write each expression with the LCD. Subtract numerators. Distribute. Combine like terms. Factor the denominators, then write down the LCD. Factor denominators.

Add or Subtract Rational Expressions with a Special Denominators Example 8 Solution Write each expression with the LCD. Distribute. Add numerators.

Example 9 Solution Problem continued on next slide…

Write each expression with the LCD. Add numerators. Distribute. Combine like terms. Factor.