Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
10th Edition
ISBN: 9780134673301
Author: Waits, Foley, Kennedy, Bock Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter P.7, Problem 10QR
Solution

Add the fraction and simplify, 2x−1x2−x−2+x−3x2−3x+2 .

  (3x+1)(x+1)(x−1)

Given:

The given fraction is, 2x−1x2−x−2+x−3x2−3x+2

Concept Used:

  • A fraction is in lowest terms when the numerator and denominator have no common factor other than 1.
  • Identify all the factors of the numerator.
  • Identify all the factors of the denominator.
  • Find the greatest common factor (GCF) of the numerator and the denominator.
  • Divide both numerator and denominator by the GCF.
  • If the fraction is improper, convert it to a mixed number.

Calculation:

   2x−1 x 2 −x−2 + x−3 x 2 −3x+2 solve   x 2 −x−2= x 2 −(2−1)x−2 = x 2 −2x+x−2 =x(x−2)+1(x−2) =(x+1)(x−2) solve  x 2 −3x+2= x 2 −3x+2 = x 2 −(2+1)x+2 = x 2 −2x−x+2 =x(x−2)−1(x−2) =(x−1)(x−2)

   put the values in above fraction − 2x−1 x 2 −x−2 + x−3 x 2 −3x+2 = 2x−1 (x+1)(x−2) + x−3 (x−1)(x−2) = (2x−1)(x−1)+(x−3)(x+1) (x+1)(x−1)(x−2) = (2x⋅x−2x⋅1−1⋅x−1⋅(−1))+(x⋅x+x⋅1−3⋅x−3⋅1) (x+1)(x−1)(x−2) = 2 x 2 −2x−x+1+ x 2 +x−3x−3 (x+1)(x−1)(x−2) = 3 x 2 −5x−2 (x+1)(x−1)(x−2)

   now  solve  3 x 2 −5x−2=3 x 2 −(6−1)x−2 =3 x 2 −6x+x−2 =3x(x−2)+1(x−2) =(3x+1)(x−2) put the value above 3 x 2 −5x−2 (x+1)(x−1)(x−2 = (3x+1)(x−2) (x+1)(x−1)(x−2) = (3x+1) (x+1)(x−1)

Thus, the simplest form of fraction is, (3x+1)(x+1)(x−1) .

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Chapter P.7, Problem 9QR
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Chapter P.7, Problem 1E

Chapter P Solutions

Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

Ch. P.1 - Prob. 1QRCh. P.1 - Prob. 2QRCh. P.1 - Prob. 3QRCh. P.1 - Prob. 4QRCh. P.1 - Prob. 5QRCh. P.1 - Prob. 6QRCh. P.1 - Prob. 7QRCh. P.1 - Prob. 8QRCh. P.1 - Prob. 9QRCh. P.1 - Prob. 10QR
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