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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 Procedure: To add or subtract fractions with like denominators. 1. Write a single fraction using the like denominator as the denominator. 2. For the numerator of the single fraction, write each of the numerators with the operation symbol between them. Note: If the operation is subtraction, and the numerator of the second fraction has more than one term, then write parentheses around around the numerator following the subtraction symbol as a reminder for distributing. 3. Simplify the numerator. 4. Factor the numerator and denominator if possible and divide out any common factors. 1. Write a single fraction using the like denominator as the denominator. 2. For the numerator of the single fraction, write each of the numerators with the operation symbol between the numerators. 3. Simplify the numerator. Your Turn Problem #1

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 2 3. Factor the numerator. 4. Divide out like factors. 1. Write a single fraction using the like denominator as the denominator. 2. For the numerator of the single fraction, write each of the numerators with the operation symbol between the numerators. Your Turn Problem #2 Answer: 6

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 3 Procedure: To add or subtract fractions with unlike denominators.Adding and Subtracting Fractions with Unlike Denominators 1. Find the LCD of the denominators. (The lowest polynomial that contains the factors of each polynomial.) 2. Multiply numerator and denominator by the same factor which makes denominator equal to the LCD (multiply only by what you need). 3. Add or subtract the numerators and combine like terms. 4. Factor the numerator and divide out the common factors if any exist. 2. Multiply numerator and denominator of 1 st fraction by 3. Multiply numerator and denominator 2 nd fraction by 4. 1. Find LCD. Your Turn Problem #3 3. Simplify.

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 4 3. Add the numerators and combine like terms. 4. Nothing to factor from numerator. 1. Find LCD. 2. Multiply numerator and denominator of 1 st fraction by 2. Multiply numerator and denominator 2 nd fraction by 3. Note: use parentheses to show distribution. Your Turn Problem #4

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 3. Add the numerators and combine like terms. 1. Find LCD. 2. Change each fraction to an equivalent fraction with a denominator of 6x 2. Your Turn Problem #5

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 3. Write as one fraction with the LCD. Distribute (don’t forget the negative). Then combine like terms. 1. Find LCD. Your Turn Problem #6

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 7 1. Find LCD. 3. Write as one fraction with the LCD. Distribute. Then combine like terms. Your Turn Problem #7

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 8 To add or subtract rational expressions where the denominator is factorable, we will have to add a step to the previous procedure. Procedure: Adding rational expressions if one or more denominators is factorable: 1. Factor each denominator 2. Continue the process given in the previous lesson. 1. Factor denominators. 2. Find LCD. 3. Change each expression to an equivalent fraction with the LCD as the denominator. 4. Combine the fractions and simplify. Your Turn Problem #8

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 9 1. Factor denominators 2. Find LCD 3. Change each expression to an equivalent fraction with the LCD as the denominator. 4. Combine the fractions and simplify. (Don’t forget to distribute the negative.) Your Turn Problem #9

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 10 1. Factor denominators 2. Find LCD 4. Combine the fractions and simplify. 3. Change each expression to an equivalent fraction with the LCD as the denominator. Your Turn Problem #10

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 11 1. Factor denominators 2. Find LCD 4. Combine the fractions and simplify. 3. Change each expression to an equivalent fraction with the LCD as the denominator. Your Turn Problem #11

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5.3 Adding and Subtracting Rational Expressions BobsMathClass.Com Copyright © 2010 All Rights Reserved. 12 1. Factor denominators 2. Find LCD 4. Combine the fractions and simplify. 3. Change each expression to an equivalent fraction with the LCD as the denominator. Your Turn Problem #12

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