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Unformatted text preview: MAC1105: Quiz #6 Solutions
July 12, 2010 In the topright corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. Simplify: 3(x2 + 3x  4) 3(x + 4)(x  1) 3(x + 4) 3x2 + 9x  12 = = = , x=1 2+x3 2x (2x + 3)(x  1) (2x + 3)(x  1) 2x + 3 x2 x2 x+6  9 x3 2. Perform the operation and simplify: First, note that x2  9 = (x + 3)(x  3), so we need to multiply the second x+3 term by x+3 to achieve a common denominator: x+6 x+3 x2 (x + 6)(x + 3) x2  = 2  x2  9 x  3 x + 3 x 9 x2  9 = x2  x2 + 9x + 18 x2  9 = 9x  18 9(x + 2) = 2 x2  9 x 9 3. Multiply the following complex rational expressions and simplify: 1+ x x x1 1 x1 1 x +2 1 x2  4 Hint: First, turn both of the complex rational expressions into simple rational expressions using the method performed in class. Then multiply them normally and simplify if needed. The common denominator in the
x 1+ x1 term is 1 x x1 x  1, so we have: 1+ x
Similarly, in the x x1 1 x1 x1 x1+x 2x  1 = = 2 x1 x(x  1)  1 x x1 x2 ,
so we have: 3 x +2 1 3 x2 term, the common denominator is 1 x +2 1 x2  4 x2 3x + 2x2 x(2x + 1) x = = = 2 x 1  4x2 (1 + 2x)(1  2x) 1  2x
1 Now the hard work is done, and our original problem becomes: (2x  1) x 2  x  1) (1  2x) (x = (1  2x)x x = 2 (x2  x  1)(1  2x) x x1 2 ...
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 Summer '10
 Picklesimer
 Algebra

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