College Algebra & Trigonometry, 2018a

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1.6. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS 59 ( 1 ( 5 1 ( 3) 2 ∗ ( 2) 3 5 = 5) 2) ∗ 5 2 2 ∗ 5 5 2 = 1 3 ∗ 5 2 1 = 1 3 ∗ 5 2 = 5 6 In this way, we can redefine division as multiplication by a reciprocal. Example Divide the expressions. Express your answer in lowest form. 2x 2 − x − 3 x 2 − x − 12 ÷ x2 +5x +4 16 − x 2 2x 2 − x − 3 x 2 − x − 12 ÷ x2 +5x +4 = 2x2 − x − 3 16 − x 2 x 2 − x − 12 ∗ 16 − x 2 x 2 +5x +4 = (2x − 3)(x +1) (x − 4)(x +3) ∗ (4 + x)(4 − x) (x +1)(x +4) = (2x − 3) ✘✘✘✘ (x +1) ✘✘✘✘ (x − 4)(x +3) ∗ ✘ (4 ✘✘✘ + x) ✘ (4✘✘✘ − x)(−1) ✘✘✘✘ (x +1) ✘ (x ✘✘✘ +4) = − 2x − 3 x +3
60 CHAPTER 1. ALGEBRA REVIEW Exercises 1.6 Reduce each expression to lowest terms. 1) 3x +9 x 2 − 9 2) 4x 2 +8x 12x +24 3) x 2 − 2x 6 − 3x 4) 15x 2 +24x 3x 2 5) 24x 2 12x 2 − 6x 6) x 2 +4x +4 x 2 − 4 7) 25 − y 2 2y 2 − 8y − 10 8) 3y 2 − y − 2 3y 2 +5y +2 9) x 2 +4x − 5 x 2 − 2x +1 10) x − x 2 x 2 + x − 2 11) x 2 +5x − 14 2 − x 12) 2x 2 +5x − 3 1 − 2x
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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2
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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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110 CHAPTER 2. POLYNOMIAL AND RATIO
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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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228 CHAPTER 4. FUNCTIONS 17) h(x) =
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230 CHAPTER 4. FUNCTIONS Original f
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232 CHAPTER 4. FUNCTIONS Then we sw
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234 CHAPTER 4. FUNCTIONS 19) f(x) =
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236 CHAPTER 4. FUNCTIONS 4.9 Optimi
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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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310 CHAPTER 7. COMBINATORICS 4) A c
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322 CHAPTER 7. COMBINATORICS SET II
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328 CHAPTER 7. COMBINATORICS Anothe
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330 CHAPTER 7. COMBINATORICS Exerci
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342 CHAPTER 7. COMBINATORICS
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344 CHAPTER 8. RIGHT TRIANGLE TRIGO
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384 CHAPTER 9. GRAPHING THE TRIGONO
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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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