document.write( "Question 742102: Respected Sir,
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Algebra.Com's Answer #452548 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "P(2n-1,n):P(2n+1,n-1) = 22:7\r\n" );
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document.write( "We can replace the colons by division symbols ÷\r\n" );
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document.write( "P(2n-1,n)÷P(2n+1,n-1) = 22÷7\r\n" );
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document.write( "P(2n-1,n)÷P(2n+1,n-1) = \"22%2F7\"\r\n" );
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document.write( "Use the formula\r\n" );
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document.write( "P(a,b) = \"a%21%2F%28a-b%29%21\"\r\n" );
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document.write( "P(2n-1,n)÷P(2n+1,n-1) = \"22%2F7\"\r\n" );
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document.write( "\"%282n-1%29%21%2F%28%282n-1%29-n%29%21\"÷\"%282n%2B1%29%21%2F%28%282n%2B1%29-%28n-1%29%29%21\" = \"22%2F7\"\r\n" );
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document.write( "Remove the inner parentheses in the denominators\r\n" );
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document.write( "\"%282n-1%29%21%2F%282n-1-n%29%21\"÷\"%282n%2B1%29%21%2F%282n%2B1-n%2B1%29%21\" = \"22%2F7\"\r\n" );
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document.write( "Simplify by combining like terms:\r\n" );
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document.write( "\"%282n-1%29%21%2F%28n-1%29%21\"÷\"%282n%2B1%29%21%2F%28n%2B2%29%21\" = \"22%2F7\"\r\n" );
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document.write( "On the left side, invert the second fraction and change \r\n" );
document.write( "division to multiplication:\r\n" );
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document.write( "\"%282n-1%29%21%2F%28n-1%29%21\"×\"%28n%2B2%29%21%2F%282n%2B1%29%21\" = \"22%2F7\"\r\n" );
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document.write( "Write (n+2)! as (n+2)(n+1)n(n-1)!\r\n" );
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document.write( "Write (2n+1)! as (2n+1)(2n)(2n-1)!\r\n" );
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document.write( "\"%282n-1%29%21%2F%28n-1%29%21\"×\"%28+%28n%2B2%29%28n%2B1%29%2An%2A%28n-1%29%21+%29%2F%28%282n%2B1%29%282n%29%282n-1%29%21%29\" = \"22%2F7\"\r\n" );
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document.write( "Cancel the (2n-1)!'s\r\n" );
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document.write( "\"cross%28%282n-1%29%21%29%2F%28n-1%29%21\"× = \"22%2F7\"\r\n" );
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document.write( "Cancel the (n-1)!'s\r\n" );
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document.write( "\"cross%28%282n-1%29%21%29%2Fcross%28%28n-1%29%21%29\"× = \"22%2F7\"\r\n" );
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document.write( "Cancel the n's\r\n" );
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document.write( "\"cross%28%282n-1%29%21%29%2Fcross%28%28n-1%29%21%29\"× = \"22%2F7\"\r\n" );
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document.write( "All that's left is\r\n" );
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document.write( "\"%28%28n%2B2%29%28n%2B1%29%29%2F%28%282n%2B1%292%29\" = \"22%2F7\"\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "7(n+2)(n+1) = 22(2n+1)2\r\n" );
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document.write( "7(n²+3n+2) = 44(2n+1)\r\n" );
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document.write( "7n²+21n+14 = 88n+44\r\n" );
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document.write( "Get 0 on the right side:\r\n" );
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document.write( "7n²-67n-30 = 0\r\n" );
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document.write( "Factor the left side as\r\n" );
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document.write( "(n-10)(7n+3) = 0\r\n" );
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document.write( "Use the zero factor property:\r\n" );
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document.write( "n-10 =  0;  7n+3 = 0\r\n" );
document.write( "   n = 10;    7n = -3\r\n" );
document.write( "               n = \"-3%2F7\"\r\n" );
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document.write( "The original problem contained permutations,\r\n" );
document.write( "which involves factorials. Only permutations\r\n" );
document.write( "and factorials involving whole numbers are \r\n" );
document.write( "defined, so we can discard the \"-3%2F7\"\r\n" );
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document.write( "Solution:  n = 10\r\n" );
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document.write( "Edwin
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