document.write( "Question 882358: sqrtx=9+4sqrt5find the value of sqrtx-1/sqrtx \n" ); document.write( "
Algebra.Com's Answer #535636 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"sqrt%28x%29=9%2B4sqrt%285%29\"\r\n" );
document.write( "\r\n" );
document.write( "find the value of \r\n" );
document.write( "\r\n" );
document.write( "\"sqrt%28x%29-1%2Fsqrt%28x%29\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute \"9%2B4sqrt%285%29\" for \"sqrt%28x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"9%2B4sqrt%285%29-+1%2F%289%2B4sqrt%285%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Rationalize the denominator of the expression on the right\r\n" );
document.write( "by multiplying by the conjugate of the denomintor over itself:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"9%2B4sqrt%285%29-+%289-4sqrt%285%29%29%2F%2881-16%2A5%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"9%2B4sqrt%285%29-+%289-4sqrt%285%29%29%2F%2881-80%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"9%2B4sqrt%285%29-+%289-4sqrt%285%29%29%2F1\"\r\n" );
document.write( "\r\n" );
document.write( "Be careful here when you drop the 1 denominator\r\n" );
document.write( "to enclose the numerator in parentheses because\r\n" );
document.write( "there are two terms and the - sign preceding it\r\n" );
document.write( "must affect both terms:\r\n" );
document.write( "\r\n" );
document.write( "\"9%2B4sqrt%285%29-+%289-4sqrt%285%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"9%2B4sqrt%285%29-+9%2B4sqrt%285%29\"\r\n" );
document.write( "\r\n" );
document.write( "The 9 and -9 cancel:\r\n" );
document.write( "\r\n" );
document.write( "\"4sqrt%285%29%2B4sqrt%285%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"8sqrt%285%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );