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

2. 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.

3. 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:

4. Common Denominator Example  Perform the indicated operations below:

5. 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.

6. 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 ___________.

7. 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.

8. Example 2  The same concept applies with subtraction.  Simplify

9. 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)

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