document.write( "Question 1192891: the numerator of a fraction is 1 less than the denominator.
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Algebra.Com's Answer #824813 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You must have copied this problem wrong, or your teacher or the\r\n" );
document.write( "the textbook writer made a mistake, for there is no solution. \r\n" );
document.write( "However, if 1/12 is changed to 1/9, there will be a solution.  \r\n" );
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document.write( "I will work a problem exactly like yours, changing 1/12 to 1/9. \r\n" );
document.write( "The problem I will work is:

\n" ); document.write( "The numerator of a POSITIVE PROPER FRACTION REDUCED TO
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document.write( "Let n = the denominator

\n" ); document.write( "The numerator of a fraction is 1 less than the denominator.
 \r\n" );
document.write( "Then the numerator = n-1\r\n" );
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document.write( "\"matrix%281%2C2%2COriginal%2CFraction%29\"\"%22%22=%22%22\"\"%28n-1%29%2Fn\"
\r
\n" ); document.write( "\n" ); document.write( "when both numerator and denominator are increased by 2,
 \r\n" );
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document.write( "\"matrix%281%2C2%2CIncreased%2CFraction%29+=+%28%28n-1%29%2B2%29%2F%28n%2B2%29\"
\r
\n" ); document.write( "\n" ); document.write( "the fraction is increased by 1/9.
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document.write( "\"matrix%281%2C2%2CIncreased%2CFraction%29\"\"%22%22=%22%22\"\"+matrix%281%2C2%2COriginal%2CFraction%29\"\"%22%22%2B%22%22\"\"expr%281%2F9%29matrix%281%2C2%2COriginal%2CFraction%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28%28n-1%29%2B2%29%2F%28n%2B2%29\"\"%22%22=%22%22\"\"%28n-1%29%2Fn\"\"%22%22%2B%22%22\"\"expr%281%2F9%29expr%28%28n-1%29%2Fn%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28n-1%2B2%29%2F%28n%2B2%29\"\"%22%22=%22%22\"\"%28n-1%29%2Fn\"\"%22%22%2B%22%22\"\"%28n-1%29%2F%289n%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28n%2B1%29%2F%28n%2B2%29\"\"%22%22=%22%22\"\"%28n-1%29%2Fn\"\"%22%22%2B%22%22\"\"%28n-1%29%2F%289n%29\"\r\n" );
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document.write( "Multiply through by the LCD = 9n(n+2)\r\n" );
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document.write( "\"9n%28n%2B1%29\"\"%22%22=%22%22\"\"9%28n%2B2%29%28n-1%29\"\"%22%22%2B%22%22\"\"%28n%2B2%29%28n-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"9n%5E2%2B9n\"\"%22%22=%22%22\"\"9%28n%5E2%2Bn-2%29\"\"%22%22%2B%22%22\"\"n%5E2%2Bn-2\"\r\n" );
document.write( "\r\n" );
document.write( "\"9n%5E2%2B9n\"\"%22%22=%22%22\"\"9n%5E2%2B9n-18%29\"\"%22%22%2B%22%22\"\"n%5E2%2Bn-2\"\r\n" );
document.write( "\r\n" );
document.write( "\"9n%5E2%2B9n\"\"%22%22=%22%22\"\"10n%5E2%2B10n-20%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"-n%5E2-n%2B20\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"n%5E2%2Bn-20\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"%28n%2B5%29%28n-4%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "n+5=0;   n-4=0\r\n" );
document.write( "  n=-5;    n=4\r\n" );
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document.write( "Ignore the negative answer.\r\n" );
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document.write( "denominator = n = 4\r\n" );
document.write( "numerator = n-1 = 4-1 = 3\r\n" );
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document.write( "original fraction = \"3%2F4\"\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "The new fraction is \"%283%2B2%29%2F%284%2B2%29\"\"%22%22=%22%22\"\"5%2F6\"\r\n" );
document.write( "\r\n" );
document.write( "\"1%2F9\" of \"3%2F4\" is \"%281%2F9%29%283%2F4%29\"\"%22%22=%22%22\"\"3%2F36\"\"%22%22=%22%22\"\"1%2F12\"\r\n" );
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document.write( "If we add \"3%2F4%2B1%2F12\"\"%22%22=%22%22\"\"9%2F12%2B1%2F12\"\"%22%22=%22%22\"\"10%2F12\"\"%22%22=%22%22\"\"5%2F6\".\r\n" );
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document.write( "So the correct answer to the problem I solved is \"3%2F4\".\r\n" );
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document.write( "Be sure to inform your teacher that the problem as stated \r\n" );
document.write( "(with 1/12) has no solution.\r\n" );
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document.write( "Edwin
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