College Algebra & Trigonometry, 2018a

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1.6. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS 61 Multiply or divide the expressions in each problem. Express your answers in lowest terms. 13) 3x +6 5x 2 ∗ x x 2 − 4 14) 4x 2 7x − 28 ∗ x 2 − 16 6x 15) 2a 2 − 7a +6 4a 2 − 9 ∗ 4a2 +12a +9 a 2 − a − 2 16) 4a 2 − 4a − 3 8a +4a 2 ∗ 16a 2 4a 2 − 6a 17) x 2 − y 2 (x + y)2 ∗ 18) (x + y) 3 (x − y) 2 2x 2 + x − 3 x 2 − 1 ∗ 2x − 2 2x 2 +5x +3 19) 6x x 2 − 4 ÷ 3x − 9 2x +4 20) 12x 5x +20 ÷ 4x2 x 2 − 16 21) 9x 2 +3x − 2 6x 2 − 2x ÷ 3x +2 6x 2 22) 2a 2 − 5a − 3 4a 2 +2a ÷ 2a +1 4a 23) x 2 +7x +6 x 2 + x − 6 ÷ x2 +5x − 6 x 2 +5x +6 24) x 2 +7x +10 x 2 − x − 30 ÷ 3x2 +7x +2 9x 2 − 1 25) 2x 2 − x − 28 3x 2 − x − 2 ÷ 4x2 +16x +7 3x 2 +11x +6 26) 9x 2 +3x − 2 12x 2 +5x − 2 ÷ 9x2 − 6x +1 8x 2 − 10x − 3
62 CHAPTER 1. ALGEBRA REVIEW 1.7 Adding and Subtracting Rational Expressions Just as we do with numerical fractions, we will need to have common denominators in order to add or subtract algebraic fractions. When we add 1 2 + 1 , we make 3 a common denominator of 6 so that we can add them together. 1 2 + 1 3 = 1 2 ∗ 3 3 + 1 3 ∗ 2 2 = 3 6 + 2 6 = 5 6 Because the denominators, 2 and 3, are prime and don’t share any common factors, the common denominator is simply 3 ∗ 2=6. We can see a similar result in adding algebraic fractions. Example Add the fractions. Express your answer in lowest terms. 2 x + x x − 3 2 x + x x − 3 = 2 x ∗ x − 3 x − 3 + = x x − 3 ∗ x x 2(x − 3) x(x − 3) + x ∗ x x(x − 3) = 2x − 6+x2 x(x − 3) = x2 +2x − 6 x(x − 3)
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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140 CHAPTER 3. EXPONENTS AND LOGARI
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190 CHAPTER 4. FUNCTIONS by substit
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192 CHAPTER 4. FUNCTIONS 4.2 Domain
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194 CHAPTER 4. FUNCTIONS Exercises
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196 CHAPTER 4. FUNCTIONS 8) 12 10 8
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198 CHAPTER 4. FUNCTIONS We can use
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200 CHAPTER 4. FUNCTIONS 3) 20 16 1
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202 CHAPTER 4. FUNCTIONS Vertical S
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204 CHAPTER 4. FUNCTIONS Now, if, i
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206 CHAPTER 4. FUNCTIONS So the gra
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208 CHAPTER 4. FUNCTIONS Stretching
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210 CHAPTER 4. FUNCTIONS Multiplyin
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214 CHAPTER 4. FUNCTIONS 3) Match e
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216 CHAPTER 4. FUNCTIONS 6) f(x) 7)
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218 CHAPTER 4. FUNCTIONS Being fami
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222 CHAPTER 4. FUNCTIONS 4.6 Piecew
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226 CHAPTER 4. FUNCTIONS 4.7 Compos
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230 CHAPTER 4. FUNCTIONS Original f
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238 CHAPTER 4. FUNCTIONS 2) The gra
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242 CHAPTER 4. FUNCTIONS 8) A recta
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244 CHAPTER 4. FUNCTIONS So, our fi
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248 CHAPTER 4. FUNCTIONS Distance O
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250 CHAPTER 4. FUNCTIONS The graph
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252 CHAPTER 4. FUNCTIONS Distance/T
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254 CHAPTER 4. FUNCTIONS The graph
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256 CHAPTER 4. FUNCTIONS 3) A power
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258 CHAPTER 5. CONIC SECTIONS - CIR
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288 CHAPTER 6. SEQUENCES AND SERIES
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306 CHAPTER 7. COMBINATORICS differ
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308 CHAPTER 7. COMBINATORICS Exampl
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344 CHAPTER 8. RIGHT TRIANGLE TRIGO
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438 CHAPTER 10. TRIGONOMETRIC IDENT
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472 CHAPTER 11. THE LAW OF SINES TH
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College Algebra & Trigonometry, 2018a

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