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Adding and Subtracting Rational Expressions Section 7.2 MATH 116-460 Mr. Keltner

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In Section 7.1… We used our knowledge of multiplying and dividing fractions to help us multiply and divide rational expressions. Now, we are going to use our knowledge of adding and subtracting fractions to help with rational expressions.

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With Common Denominators As with numerical fractions, the process used to add (or subtract) two rational expressions depends on whether they have like or unlike denominators. We first look at when they have like denominators. Try this example with fractions:

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Common Denominator Example Perform the indicated operations below:

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Fraction Example If we add two fractions with unlike denominators, like First we need to look for a common denominator, which in this case would be ______. We then multiply each fraction by a convenient way to write 1, such that each denominator will be the same.

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Using that idea Use that same knowledge for finding a least common denominator to simplify the rational expression Our common denominator in this case would be ____________, or ___________.

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Example 1, Cont. Now that we have a common denominator, we can combine like terms and simplify. Check to see if we can divide out a common factor on top and bottom. This is simplified, since there are no common factors to divide out.

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Example 2 The same concept applies with subtraction. Simplify

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A couple things to be careful of… You must be careful with signs when using subtraction because of the way the distributive property works. Some examples: 4 - (x - 9) ≠ 4 - x - 9 2x - ( -3x) ≠ -1x 2(x - 4) - (x - 4)(x + 2) ≠ 2(x - 4) - x - 4(x + 2)

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Assessment Pgs. 472-475: #’s 9 - 90, multiples of 9

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