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.5, Problem 10QR
Solution

To combine and reduce the fraction to lowest form, x+1x2−5x+6−3x+11x2−x−6 .

  −2(x+4)(x−2)(x+2)

Given:

The given fraction is, x+1x2−5x+6−3x+11x2−x−6

Concept Used:

  • 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:

   x+1 x 2 −5x+6 − 3x+11 x 2 −x−6 first solve   x 2 −5x+6                 x 2 −(3+2)x+6                x 2 −3x−2x+6              x(x−3)−2(x−3)             (x−2)(x−3) then solve   x 2 −x−6                        x 2 −(3−2)x−6                       x 2 −3x+2x−6                      x(x−3)+2(x−3)                      (x+2)(x−3) put these values

   x+1 (x−2)(x−3) − 3x+11 (x+2)(x−3) = (x+1)(x+2)−(3x+11)(x−2) (x−2)(x+2)(x−3) ( x 2 +2x+x+2)−(3 x 2 −6x+11x−22) (x−2)(x+2)(x−3) x 2 +2x+x+2−3 x 2 +6x−11x+22 (x−2)(x+2)(x−3) −2 x 2 −2x+24 (x−2)(x+2)(x−3)

   now solve (−2 x 2 −2x+24)   −2 x 2 −2x+24  −2( x 2 +x+12) −2( x 2 +4x−3x+12) −2(x(x+4)−3(x+4)) −2(x−3)(x+4) put this value above

   −2(x−3)(x+4) (x−2)(x+2)(x−3) = −2(x+4) (x−2)(x+2) = −2(x+4) (x−2)(x+2)

Thus, the lowest form of fraction is,, −2(x+4)(x−2)(x+2) .

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Chapter P.5, Problem 9QR
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Chapter P.5, 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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P.6 - Prob. 53ECh. P.6 - Prob. 54ECh. P.6 - Prob. 55ECh. P.6 - Prob. 56ECh. P.6 - Prob. 57ECh. P.7 - Prob. 1QRCh. P.7 - Prob. 2QRCh. P.7 - Prob. 3QRCh. P.7 - Prob. 4QRCh. P.7 - Prob. 5QRCh. P.7 - Prob. 6QRCh. P.7 - Prob. 7QRCh. P.7 - Prob. 8QRCh. P.7 - Prob. 9QRCh. P.7 - Prob. 10QRCh. P.7 - Prob. 1ECh. P.7 - Prob. 2ECh. P.7 - Prob. 3ECh. P.7 - Prob. 4ECh. P.7 - Prob. 5ECh. P.7 - Prob. 6ECh. P.7 - Prob. 7ECh. P.7 - Prob. 8ECh. P.7 - Prob. 9ECh. P.7 - Prob. 10ECh. P.7 - Prob. 11ECh. P.7 - Prob. 12ECh. P.7 - Prob. 13ECh. P.7 - Prob. 14ECh. P.7 - Prob. 15ECh. P.7 - Prob. 16ECh. P.7 - Prob. 17ECh. P.7 - Prob. 18ECh. P.7 - Prob. 19ECh. P.7 - Prob. 20ECh. P.7 - Prob. 21ECh. P.7 - Prob. 22ECh. P.7 - Prob. 23ECh. P.7 - Prob. 24ECh. P.7 - Prob. 25ECh. P.7 - Prob. 26ECh. P.7 - Prob. 27ECh. P.7 - Prob. 28ECh. P.7 - Prob. 29ECh. P.7 - Prob. 30ECh. P.7 - Prob. 31ECh. P.7 - Prob. 32ECh. P.7 - Prob. 33ECh. P.7 - Prob. 34ECh. P.7 - Prob. 35ECh. P.7 - Prob. 36ECh. P.7 - Prob. 37ECh. P.7 - Prob. 38ECh. 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P - Prob. 44RECh. P - Prob. 45RECh. P - Prob. 46RECh. P - Prob. 47RECh. P - Prob. 48RECh. P - Prob. 49RECh. P - Prob. 50RECh. P - Prob. 51RECh. P - Prob. 52RECh. P - Prob. 53RECh. P - Prob. 54RECh. P - Prob. 55RECh. P - Prob. 56RECh. P - Prob. 57RECh. P - Prob. 58RECh. P - Prob. 59RECh. P - Prob. 60RECh. P - Prob. 61RECh. P - Prob. 62RECh. P - Prob. 63RECh. P - Prob. 64RECh. P - Prob. 65RECh. P - Prob. 66RECh. P - Prob. 67RECh. P - Prob. 68RECh. P - Prob. 69RECh. P - Prob. 70RECh. P - Prob. 71RECh. P - Prob. 72RECh. P - Prob. 73RECh. P - Prob. 74RECh. P - Prob. 75RECh. P - Prob. 76RECh. P - Prob. 77RECh. P - Prob. 78RECh. P - Prob. 79RECh. P - Prob. 80RECh. P - Prob. 81RECh. P - Prob. 82RECh. P - Prob. 83RE
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