Adding and Subtracting Rational Expressions MATH 017 Intermediate Algebra S. Rook

2 Overview Section 6.2 in the textbook –Add and subtract rational expressions with like denominators –Find the LCD of two rational expressions –Add and subtract rational expressions with unlike denominators

Add or Subtract Like Denominators

4 Consider adding 1 / / 10 –Denominators are the same – add the numerators and keep the denominator 4 / 10 –Simplify the final answer if possible 2 / 5

5 Add and Subtract Like Denominators (Continued) Similar for rational expressions with equal denominators –Add the polynomial numerators and keep the polynomial denominator –Simplify the final answer if possible

6 Add and Subtract Like Denominators (Example) Ex 1: Add or subtract and then simplify

7 Add and Subtract Like Denominators (Example) Ex 2: Add or subtract and then simplify

LCD of Rational Expressions

9 Least Common Denominator (LCD): the smallest product of factors that each denominator will divide into evenly –Factor all the denominators –Find the numerical LCD –Find the variable LCDs Take the variable raised to the HIGHEST power –Factors in the LCD do not necessarily have to be monomials

10 LCD of Rational Expressions (Example) Ex 3: Find the LCD

11 LCD of Rational Expressions (Example) Ex 4: Find the LCD

12 LCD of Rational Expressions (Example) Ex 5: Find the LCD

13 LCD of Rational Expressions (Example) Ex 6: Find the LCD

Add and Subtract Unlike Denominators

15 Add and Subtract Unlike Denominators Consider adding 2 / / 6 –Denominators are NOT the same Must find the LCD between 3 and 6 3 = 3, 6 = 2 * 3 → LCD = 2 * 3 = 6 –What factors in the LCM are missing from both denominators? Multiply both numerator and denominator by these factors (2 / 2) * (2 / 3) + (1 / 6) * (1 / 1) 4 / / 6 5 / 6

16 Add and Subtract Unlike Denominators (Continued) Same process for adding rational expressions –Factor the denominators –Find the LCD –Multiply both numerator and denominator by missing factors in the LCD –Simplify

17 Add and Subtract Unlike Denominators (Example) Ex 7: Add

18 Add and Subtract Unlike Denominators (Example) Ex 8: Add

19 Add and Subtract Unlike Denominators (Example) Ex 9: Subtract

20 Add and Subtract Unlike Denominators (Example) Ex 10: Subtract

21 Summary After studying these slides, you should know how to do the following: –Add and subtract rational expressions with the same denominator –Identify the LCD (Least Common Denominator) between two rational expressions –Add and subtract rational expressions with unlike denominators