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X2 4x 5 x 4 x 2 x 2 when numbers are reversed

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Unformatted text preview: g the largest common factor in both cases, we have 3b 2 ( b + 2 ) 4b ( b + 2) 4 b 2 + 8b 3b 3 + 6b 2 The factors common to both numerator and denominator are b and (b + 2). Dividing these out, we have Example: Simplify Solution: There are no common factors here, but both numerator and denominator may be factored as 4 . 3b x 2 + 6x + 8 to simplest form. x 2 + x − 12 trinomials. x + 4 x − 3 gives x − 3 as a final answer. Remember not to cancel the x’s as they are ( )( ) () terms and not factors. Example: Simplify Solution: The numerator contains a common factor, while the denominator must be factored as a trinomial. 5− x 2 ( x − 5)( x + 1) 10 − 2 x to simplest form. x2 − 4x − 5 ( x + 4)( x + 2) ( x + 2) When numbers are reversed around a minus sign, they may be turned around by factoring out a (–1).5 – x = (– 1)(x – 5). Doing this will enable us to simplify the fraction to reversed around a plus sign, the factors could have been divided without factoring further, as a + b = b + a, by the cummutative law of addition. Subtraction, however, is not commutative, necessitating the factoring of –1. −2 . Remember that if the terms had been x +1 www.petersons.com 158 Chapter 11 Exercise 1 Work out each problem. Circle the letter that appears before your answer. 1. 3x 3 − 3x 2 y Simplify to simplest form: 9 x 2 − 9 xy x (A) 6 x (B) 3 2x (C) 3 4. Simplify to simplest form: (A) (B) (C) (D) (E) 4 5 − 4 3 b+4 b+5 b−4 b−5 b+4 − b+5 b 2 + b − 12 b 2 + 2b − 15 (D) (E) 2. 1 x−y 3 Simplify to simplest form: (A) (B) (C) (D) (E) 2 − 3 2 3 4 − 3 4 3 3 − 2 3x − y 2x − 8 12 − 3x 5. Simplify to simplest form: 6 x + 12 y (A) (B) (C) (D) 2 3 − 2 3 1 − 3 1 3 2x + 4 y 3. Find the value of y − 3 x when x = and 7 3 . 10 24 (A) 70 11 (B) 70 y= 2 (E) 3 (C) (D) (E) 0 1 –1 www.petersons.com Factoring and Algebraic Fractions 159 2. ADDITION OR SUBTRACTION OF FRACTIONS In adding or subtracting fractions, it is necessary to have the fractions expressed in terms of the same common denominator. When adding or subtracting...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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