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A b c d e 100 20 40 60 80 10 the trinomial x2 x

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Unformatted text preview: o a single fraction: 2 − (A) (B) (C) (D) (E) 2−a b 2−a 2−b a − 2b b 2b − a b 2a − b b x−5 5− x by . x+5 5+ x a . b 5. 1 Simplify 2 + a b a 2a + 1 (A) b (B) (C) (D) (E) 2a + 1 a 2a + 1 ab 4a2 + 1 xy 2b + 1 b 3. Divide (A) (B) (C) (D) (E) 1 –1 ( x − 5 )2 ( x + 5 )2 ( x − 5 )2 − ( x + 5 )2 0 155 156 Chapter 11 11 − ab Simplify 2 b−a (A) 2 a−b (B) 2 b−a (C) 2ab ba (D) 2 2ab (E) b+a 6. 9. If x + y = 2 and x − y = 4 , find x 2 − y 2 (A) (B) (C) (D) (E) 3 4 1 4 3 16 1 8 7 8 1 1 1 1 1 1 1 1 7. If x + y = 16 and x2 – y2 = 48, then x – y equals (A) 3 (B) 32 (C) 4 (D) 36 (E) 6 If (x + y)2 = 100 and xy = 20, find x2 + y2. (A) (B) (C) (D) (E) 100 20 40 60 80 10. The trinomial x2 – x – 20 is exactly divisible by (A) x – 4 (B) x – 10 (C) x + 4 (D) x – 2 (E) x + 5 8. www.petersons.com Factoring and Algebraic Fractions 157 1. SIMPLIFYING FRACTIONS In simplifying fractions, we must divide the numerator and denominator by the same factor. We can multiply or divide both the numerator and denominator of a fraction by the same number without changing the value of the fraction. However, if we were to add or subtract the same number in the numerator and denominator, the value of 9 3 9 3⋅3 = to , we are really saying that and then 12 4 12 3 ⋅ 4 9 5+ 4 94 = = . This is dividing the numerator and denominator by 3. We may not say that and then say that 12 5 + 7 12 7 9t 3 9+t = because we divide numerator and denominator by 3t. However, a serious error in algebra as well. 12t 4 12 + t the fraction would not remain the same. When we simplify cannot be simplified, as there is no factor that divides into the entire numerator as well as the entire denominator. Never cancel terms! That is, never cancel parts of numerators or denominators containing + or – signs unless they are enclosed in parentheses as parts of factors. This is one of the most frequent student errors. Be very careful to avoid it. Example: Simplify Solution: Factoring the numerator and denominator by removin...
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