First Principles of Algebra; Complete Course

First Principles of Algebra; Complete Course

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1912 edition. Excerpt: ...+ 1) _(x-l)(x-l)_a: a-2;r + l (a;-5)(a; + l) a;2-4a: -5 It is desirable to resolve each numerator and denominator into prime factors, and then cancel all common factors before performing any multiplication. EXERCISES Find the following indicated products and reduce each fraction to its lowest terms: 3sY 6az 12c36 35(c+cb + b) '2yz 9 a?5' 'S-fe3) 14 c262 5a(a-b) 9(a + b) gM-3y+2 y-7y+12 '3c(a + 6) 15(a-b) 'y-5y+Q y+Sy+7' EXERCISES Perform the following indicated divisions, and reduce the resulting fractions to their lowest terms:, as + b3. a + b ari-6a;-16. i + 9a;+14 COMPLEX FRACTIONS 216. Sometimes fractions occur whose numerators or denominators, or both, contain fractions. i + l JL. +-1 a x--1 x + 1 Such fractions are called complex fractions. A complex fraction is said to be simplified when it is reduced to an equal fraction whose numerator and denominator are in the integral form. 1+1 "+1 _.. a a a + 1 a--1 a + 1 JiiX. 1. T = Z = = 1 1 _i a a a a--1 a a This result may also be obtained directly by multiplying both terms of the given fraction by a, finding at once a a?-l 2 By multiplying the terms of the given fraction by (x + 1) (x--1) we may also get directly----2--= x. x + 1--x + 1 Make a rule for finding the expression by which numerator and denominator of a complex fraction may be multiplied so as to reduce it directly to a simple fraction. Apply this rule to each of the following. Ex. 1. h +. Ex. 2. i i i. S J 1 I t tf EXERCISES Reduce each of the following complex fractions to its simplest form: x 1 + x m + n + 1 a"--8 b3 1 +1 4. 3 7.-; 13. A picture inside the frame is 12 inches long and 8 inches wide. If the frame is a inches wide, express its area in terms of a. 14. If h is the length of more

Product details

  • Paperback | 84 pages
  • 189 x 246 x 4mm | 168g
  • United States
  • English
  • black & white illustrations
  • 1236911474
  • 9781236911476