document.write( "Question 72722This question is from textbook Algebra:Structure and Method
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Algebra.Com's Answer #52011 by rmromero(383) $\"\"$ $\"About$
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document.write( "Solve the problem 
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document.write( "     20        4
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document.write( "    ____  -   ____  = 3/2
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document.write( "    3n+1      3n-1\r
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document.write( "Find the LCD of 3n + 1 nd 3n - 1
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document.write( " LCD = (3n + 1)(3n - 1)
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document.write( "Multiply the LCD both sides\r
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document.write( "                      20        4
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document.write( "[(3n + 1)(3n - 1)]   ____  -   ____  = 3/2  [(3n + 1)(3n - 1)]
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document.write( "                     3n+1      3n-1\r
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document.write( "      20 (3n - 1) - 4(3n + 1) = 3/2 (3n + 1)(3n - 1)\r
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document.write( "Simplify:
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document.write( "     [20(3n) - 20 (1)] - [4(3n) + 4(1)] = 3/2(9n^2 - 1)
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document.write( "   48n - 24 = (27/2)n^2 - 3/2
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document.write( "Multiply 2 both sides\r
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document.write( "   96n - 48 = 27n^2 - 3\r
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document.write( "          0 = 27n^2 - 96n + 45
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document.write( "Factor
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document.write( "          0 = (9n - 5)(3n - 9)     \r
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document.write( "Apply zero product property\r
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document.write( "      9n - 5 = 0       and      3n - 9 = 0
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document.write( "         9n  = 5                    3n = 9
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document.write( "          n  = 5/9                   n = 3\r
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document.write( "If you want to see if the values of your n are correct, 
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document.write( "substitute n = 5/9 and n = 3 to the equation.         \r
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document.write( "Checking \r
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document.write( "     20        4
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document.write( "    ____  -   ____  = 3/2
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document.write( "    3n+1      3n-1\r
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document.write( "When n = 5/9\r
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document.write( "        20            4
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document.write( "    ________  -   ________  = 3/2
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document.write( "    3(5/9)+1      3(5/9)-1\r
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document.write( "      20         4
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document.write( "    _____  -   ______  = 3/2
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document.write( "    5/3+1      5/3-1\r
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document.write( "     20        4
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document.write( "    ____  -   ____  = 3/2
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document.write( "     8/3       2/3 \r
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document.write( "    20*3       4*3
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document.write( "   ______  -  _____  = 3/2
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document.write( "     8          2\r
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document.write( "      60      12      3
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document.write( "    _____  - ___  = ____  
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document.write( "      8       2       2\r
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document.write( "     30         3
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document.write( "    ____ - 6 = ___
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document.write( "     4          2\r
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document.write( "     30     24    3
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document.write( "    ____ - ___ = ___
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document.write( "     4      4     2\r
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document.write( "        6      3
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document.write( "       ___  = ___
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document.write( "        4      2\r
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document.write( "       3/2 = 3/2  ------> True\r
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document.write( "When n = 3\r
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document.write( "      20        4
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document.write( "    ____  -   ______  = 3/2
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document.write( "    3(3)+1    3(3)-1\r
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document.write( "      20        4
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document.write( "    ____  -   ______  = 3/2
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document.write( "    9 + 1      9 -1\r
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document.write( "     20         4
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document.write( "    ____  -   ______  = 3/2
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document.write( "     10         8\r
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document.write( "     2 - 1/2  = 3/2\r
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document.write( "    4       1
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document.write( "   ___  -  ___ = 3/2
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document.write( "    2       2\r
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document.write( "      3/2 = 3/2   ------> True\r
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document.write( "Therefore the solutions are n = 5/9 and n = 3 \n" );
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