College Algebra & Trigonometry, 2018a

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1.5. QUADRATIC EQUATIONS WITH COMPLEX ROOTS 53 Exercises 1.5 Solve for x in each equation. Round any irrational values to the nearest 1000th. 1) 3x 2 − 3x =4 2) 4x 2 − 2x =7 3) 5x 2 =3− 7x 4) 3x 2 =21− 14x 5) 6x 2 +1=2x 6) 5x − 3x 2 =17 7) (5x − 1)(2x +3)=3x − 20 8) (x + 4)(3x − 1) = 9x − 5 9) (x − 2) 2 =8x(x − 1) + 10 10) (2x − 3) 2 =2x − 7x 2 11) (x +5)(x − 6) = (2x − 1)(x − 4) 12) (3x − 4)(x +2)=(2x − 5)(x +5)
54 CHAPTER 1. ALGEBRA REVIEW 1.6 Multiplying and Dividing Rational Expressions Reducing Rational Expressions A rational expression is simply an algebraic fraction, and our first consideration will be to reduce these expressions to lowest terms in the same way that we reduce numerical fractions to lowest terms. When we reduce 6 15 to 2 by canceling 5 the common factor of three, we are removing a redundant factor of 1 in the form of 3 3 . 6 15 = 3 ∗ 2 3 ∗ 5 = 3 3 ∗ 2 5 =1∗ 2 5 = 2 5 Similarly, if there is a common factor that can be factored out of an algebraic fraction, this also can be canceled. 21x +14 7x +7 = 7(3x +2) 7(x +1) = 7 7 =1∗ ∗ 3x +2 x +1 3x +2 x +1 = 3x +2 x +1 It’s important to remeber that only common factors can be canceled. This means
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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Page 7 and 8: 4 CONTENTS 2.4 Solution of Rational
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104 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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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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322 CHAPTER 7. COMBINATORICS SET II
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328 CHAPTER 7. COMBINATORICS Anothe
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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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