76 CHAPTER R Review of Basic Concepts EXAMPLE 4 Adding or Subtracting Rational Expressions Add or subtract, as indicated. (a) 5 9x2 + 1 6x (b) y y - 2 + 8 2 - y (c) 3 x2 + x - 2 - 1 x2 - x - 12 SOLUTION (a) 5 9x2 + 1 6x Step 1 Write each denominator as a product of prime factors. 9x2 = 32 # x2 6x = 21 # 31 # x1 Step 2 For the LCD, form the product of all the prime factors, with each factor having the greatest exponent that appears on it. Greatest exponent on 3 is 2. Greatest exponent on x is 2. LCD= 21 # 32 # x2 = 18x2 Write the given expressions with this denominator, and then add. 5 9x2 + 1 6x = 5 # 2 9x2 # 2 + 1 # 3x 6x # 3x LCD= 18x2 = 10 18x2 + 3x 18x2 Multiply. = 10 + 3x 18x2 Add the numerators. Always check to see that the answer is in lowest terms. (b) y y - 2 + 8 2 - y We arbitrarily choose y - 2 as the LCD. = y y - 2 + 81-12 12 - y21-12 Multiply the second expression by -1 in both the numerator and the denominator. = y y - 2 + -8 y - 2 Simplify. = y - 8 y - 2 Add the numerators. We could use 2 - y as the common denominator instead of y - 2.
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