# Chapter 6 Section 3 Adding and Subtracting of Rational Expressions with a Common Denominator 1.

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Chapter 6 Section 3 Adding and Subtracting of Rational Expressions with a Common Denominator 1

Add or Subtract two Fraction with a Common Denominator Add two Fractions with a Common Denominator Example: Subtract two Fractions with a Common Denominator. Make sure you subtract the entire numerator of the fraction 2

 Add or subtract the numerator.  Place the sum or difference of the numerators over the common denominator.  Simplify the fraction if possible. Add or Subtract Rational Expressions with a Common Denominator 3

Example: Add Rational Expressions with a Common Denominator Write as a single fraction Drop the parentheses Combine like term 4

Example: Add Rational Expressions with a Common Denominator Write as a single fraction and drop the parentheses in the numerator Combine like term Factor and divide out any common factors. GCF = 3x 5

Example: Add Rational Expressions with a Common Denominator Write as a single fraction and drop the parentheses in the numerator Combine like terms Factor and divide out common factors. 6 Factors of 7 the add to 8 (1)(7) = 7 and (1) + (7) = 8

Example: Subtract Rational Expressions with a Common Denominator Write as a single fraction and Remove the parentheses in the numerator. Combine like terms Factor and divide out common factors. 7 NOTE: all the signs of the terms being subtracted change. When only the signs differ in a numerator and denominator factor out -1

Subtract Rational Expressions with a Common Denominator Factor out a -1, then 4m 2 + 17m + 4 8 Write as a single fraction and Remove the parentheses in the numerator. Combine like terms Factor and divide out common factors. NOTE: all the signs of the terms being subtracted change. (a)(c) = (4)(4) = 16 Factors of 16 sum to 17 (1)(16)=16 and (1)+(16)=17 Replace the 17m with 1m and 16m and Factor by grouping

Least Common Denominator  Factor each denominator completely. Any factor occurring more than once should be expressed in powers. (x-3)(x-3) = (x-3) 2  List all different factors that appear  LCD is the product of all factors listed 9

Example: Finding the Least Common Denominator 10

Example: Finding the Least Common Denominator 11

Finding the Least Common Denominator The Least Common Denominator is the product of the highest power of each factor in any of the denominators. 1.Factor each denominator completely. Any factors that occur more than once should be expressed as powers. (x-3)(x-3) = (x-3) 2 2.List all the factors, other than 1, that appear. When appears in highest power 3.LCD is the product of all the powers listed. 12

Example: Finding the Least Common Denominator 13 Remember for the LCD we use the highest power and multiply them together.

Example: Finding the Least Common Denominator 14 LCD use the highest power and multiply them together.

Example: Finding the Least Common Denominator 15

Example: Finding the Least Common Denominator 16

Example: Finding the Least Common Denominator 17

Example: Finding the Least Common Denominator 18 Same Factors of -32 that sum to 4 (8)(-4) = -32 and (8)+(-4)=4

Remember  When subtracting, you must subtract the entire numerator of the fraction that follows the minus sign by applying the distributive property. In other words, change the sign of all the second terms in the numerator when subtracting.  The Least Common Denominator is the product of the highest power of each factor in any of the denominators.  Simplify your final answers. 19

HOMEWORK 6.3 Page 373-374: #15, 19, 33, 45, 53, 57, 77, 81, 85 20

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