document.write( "Question 945597: Solve the equation \"%28matrix%282%2C1%2Cn%2C2%29%29\"\"%22%22-%22%22\"\"%28matrix%282%2C1%2Cn%2C1%29%29\"\"%22%22=%22%22\"\"20\"
\n" ); document.write( "where n is a natural number\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #576871 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"%28matrix%282%2C1%2Cn%2C2%29%29\"\"%22%22-%22%22\"\"%28matrix%282%2C1%2Cn%2C1%29%29\"\"%22%22=%22%22\"\"20\"\r\n" );
document.write( "\r\n" );
document.write( "\"n%21%2F%282%21%2A%28n-2%29%21%29\"\"%22%22-%22%22\"\"n%21%2F%281%21%2A%28n-1%29%21%29\"\"%22%22=%22%22\"\"20\"\r\n" );
document.write( "\r\n" );
document.write( "Replace n! by n*(n-1)*(n-2)! in the first fraction and by n*(n-1)! in the second \r\n" );
document.write( "\r\n" );
document.write( "\"%28n%2A%28n-1%29%2A%28n-2%29%21%29%2F%282%2A%28n-2%29%21%29\"\"%22%22-%22%22\"\"%28n%2A%28n-1%29%21%29%2F%281%28n-1%29%21%29\"\"%22%22=%22%22\"\"20\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28n%2A%28n-1%29%2Across%28%28n-2%29%21%29%29%2F%282%2Across%28%28n-2%29%21%29%29\"\"%22%22-%22%22\"\"%28n%2Across%28%28n-1%29%21%29%29%2F%281cross%28%28n-1%29%21%29%29\"\"%22%22=%22%22\"\"20\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28n%2A%28n-1%29%29%2F2\"\"%22%22-%22%22\"\"n%2F1\"\"%22%22=%22%22\"\"20\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 2 to clear of fractions:\r\n" );
document.write( "\r\n" );
document.write( "\"n%2A%28n-1%29-2n\"\"%22%22=%22%22\"\"40\"\r\n" );
document.write( "\r\n" );
document.write( "\"n%5E2-n-2n\"\"%22%22=%22%22\"\"40\"\r\n" );
document.write( "\r\n" );
document.write( "\"n%5E2-3n\"\"%22%22=%22%22\"\"40\"\r\n" );
document.write( "\r\n" );
document.write( "\"n%5E2-3n-40\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28n-8%29%28n%2B5%29\"\"%22%22=%22%22\"\"%220%22\"\r\n" );
document.write( "\r\n" );
document.write( "n-8 = 0;  n+5 = 0\r\n" );
document.write( "  n = 8     n = -5\r\n" );
document.write( "\r\n" );
document.write( "Ignore negative answer.\r\n" );
document.write( "\r\n" );
document.write( "Answer:  n = 8\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "
\n" ); document.write( "
\n" );