• Document: Section 7.4: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH DIFFERENT DENOMINATORS
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INTERMEDIATE ALGEBRA WORKBOOK/FOR USE WITH ROBERT BLITZER’S TEXTBOOK INTRODUCTORY AND INTERMEDIATE ALGEBRA FOR COLLEGE STUDENTS, 4TH ED. Section 7.4: ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH DIFFERENT DENOMINATORS When you are done with your homework you should be able to…  Find the least common denominator  Add and subtract rational expressions with different denominators WARM-UP: Perform the indicated operation and simplify. 3 5 x2 1 a.  b.  8 12 x2  x x2  x FINDING THE LEAST COMMON DENOMINATOR (LCD) The _______________ ________________ denominator of several _______________ _________________ is a _________________ consisting Of the _______________ of all _________________ _______________ in the __________________, with each ______________ raised to the greatest _______________ of its occurrence in any denominator. CREATED BY SHANNON MARTIN GRACEY 1 FINDING THE LEAST COMMON DENOMINATOR 1. _______________ each _____________ completely. 2. List the factors of the first ______________________. 3. Add to the list in step 2 any ________________ of the second denominator that do not appear in the list. Repeat this step for all denominators. 4. Form the ________________ of the ________________ from the list in step 3. This product is the LCD. Example 1: Find the LCD of the rational expressions. 11 17 7 12 a. and 2 and 2 25 x 2 35 x b. y  49 y  14 y  49 ADDING AND SUBTRACTING RATIONAL EXPRESSIONS THAT HAVE DIFFERENT DENOMINATORS 1. Find the _________ of the _________________ __________________. 2. Rewrite each rational expression as an _________________ expression whose _________________ is the ___________. 3. Add or subtract ________________, placing the resulting expression over the LCD. 4. If possible, _______________ the resulting rational expression. CREATED BY SHANNON MARTIN GRACEY 2 Example 2: Add or subtract as indicated. Simplify the result, if possible. 5 7 a.  6 x 8x 1 b. 3  x 2 x c.  3x x  3 y y 5 d.  y 5 y CREATED BY SHANNON MARTIN GRACEY 3 3x  7 3 e.  x2  5x  6 x  3 5 3 f.  x  36  x  6 2 2 ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WHEN DENOMINATORS CONTAIN OPPOSITE FACTORS When one denominator contains the _____________ factor of the other, first ________________ either rational expression by __________. Then apply the ________________ for _______________ or _______________ rational expressions that have ________________ ____________________. CREATED BY SHANNON MARTIN GRACEY 4 Example 3: Add or subtract as indicated. Simplify the result, if possible. x7 x a.  4 x  12 9  x 2 5x 2 b. 2 2  x y yx 7y 2 2y y 1 c. 2   y  y  12 4  y y  3 CREATED BY SHANNON MARTIN GRACEY 5 Section 7.5: COMPLEX RATIONAL EXPRESSIONS When you are done with your homework you should be able to…  Simplify complex rational expressions by dividing  Simplify complex rational expressions by multiplying by the LCD WARM-UP: Perform the indicated operation. Simplify, if possible. x  1 3x x 2  x 12 x a.  b. 2  x x 1 x  4 2x  4 SIMPLIFYING A COMPLEX RATIONAL EXPRESSION BY DIVIDING 1. If necessary, add or subtract to get a ____________ rational expression in the _________________. 2. If necessary, add or subtract to get a ____________ rational expression in the _________________. 3. Perform the _________________ indicated by the main ______________ bar: _______________ the denominator of the complex rational expression and _________________. 4. If possible, _______________. CREATED BY SHANNON MARTIN GRACEY 6 Let’s simplify the problem below using this method: 1 2  2 3 2

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