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4 5 c d 4 5 e e 2 1 a b a multiply every term

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Unformatted text preview: (C) x – 2 (D) x – 10 (E) x – 1 If 1 1 11 11 − = 6 and + = 5 , find 2 − 2 . ab ab a b 8. 4. 5a 3 Find an expression equivalent to b . (A) (B) (C) (D) (E) 15a 6 b3 15a 9 b3 125a 6 b3 125a 9 b3 25a 6 b3 9. (A) (B) (C) (D) (E) 30 –11 61 11 1 10. If (x – y)2 = 30 and xy = 17, find x2 + y2. (A) –4 (B) 4 (C) 13 (D) 47 (E) 64 www.petersons.com 166 Chapter 11 SOLUTIONS TO PRACTICE EXERCISES Diagnostic Test 1. 2. 3. (C) (D) (B) 3n + 8n 11n = 12 12 2 a 2b − a −= 1b b Exercise 1 1. 2. 3. (B) (A) (E) 3 x 2 ( x − y) x = 9 x ( x − y) 3 x −5 5+ x ⋅ cancel x + 5’s. x +5 5− x x−5 x−5 = = −1 5 − x −1( x − 5) 3x 2 3x 2 3x 2 27 x 6 ⋅ ⋅ =3 y y y y 2( x − 4) 2 =− 3(4 − x ) 3 3x − y = −1 regardless of the values of x y − 3x (b + 4)(b − 3) (b + 4) = (b + 5)(b − 3) (b + 5) 2( x + 2 y) 2 1 == 6( x + 2 y) 6 3 and y, as long as the denominator is not 0. 4. 5. (C) (D) 4. 5. (E) (E) 2+ 1 a b a Multiply every term by a. = 2+ 1a ⋅ ab = 2+ 1 2b + 1 = b b 6. (C) b−a 2ab Multiply every term by ab. 7. (A) x2 – y2 = (x + y) (x – y) = 48 Substituting 16 for x + y, we have 16( x − y) = 48 x−y=3 8. (D) (x + y)2 = x2 + 2xy + y2 = 100 Substituting 20 for xy, we have x 2 + 40 + y 2 = 100 x 2 + y 2 = 60 9. (D) 1 1 1 1 1 1 x + y x − y = 2 − 2 x y 1 1 1 1 2 4 = 2 − 2 x y 11 1 − = 8 x 2 y2 10. (C) x2 – x – 20 = (x – 5)(x + 4) www.petersons.com Factoring and Algebraic Fractions 167 Exercise 2 1. (D) = 6x + 5y 4 x + y − 2x 2x Exercise 3 1. (B) Divide x2 and y3. 6 x + 5y − 4 x − y 2 x + 4 y = 2x 2x 2( x + 2 y) x + 2 y = = 2x x y 1y ⋅= 1 x3 x3 2. 3. 4. (C) (C) (D) 2c ⋅ c⋅ 2. 3. 4. 5. (D) (B) (A) (C) 3c + 3d 3(c + d ) = =3 c+d c+d 2a + 3a 5a a = = 10 10 2 x +4+3 x +7 = 6 6 3b(10) − 4(7b) 30 b − 28b = 4(10) 40 2b b = = 40 20 b =b c ax y a ⋅ Divide y and x. by x b 3d 2 Divide 2, a, and b. 2a 2 b 4 abc ⋅ 3d 2 6cd 2 = a a 5. (A) 3a 2 c 4 1 ⋅ Divide 3, a, and c2. 4 b 2 6ac 2 ac 2 1 ac 2 ⋅= 4 b 2 2 8b 2 www.petersons.com 168 Chapter 11 Exercise 4 1. (E) Multiply e...
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