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Quiz6solutions - MAC1105: Quiz #6 Solutions July 12, 2010...

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Unformatted text preview: MAC1105: Quiz #6 Solutions July 12, 2010 In the top-right 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+x-3 2x (2x + 3)(x - 1) (2x + 3)(x - 1) 2x + 3 x2 x2 x+6 - -9 x-3 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 x-1 1 x-1 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+ x-1 term is 1 x- x-1 x - 1, so we have: 1+ x- Similarly, in the x x-1 1 x-1 x-1 x-1+x 2x - 1 = = 2 x-1 x(x - 1) - 1 x -x-1 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 -x-1 2 ...
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Quiz6solutions - MAC1105: Quiz #6 Solutions July 12, 2010...

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