document.write( "Question 146052: the problem:\r
\n" ); document.write( "\n" ); document.write( "1/2 + 3/x = x+6/2x\r
\n" ); document.write( "\n" ); document.write( "How does the x get from denominator to numerator? I'm not sure how to work the problem to get the x on top.\r
\n" ); document.write( "\n" ); document.write( "Please help explain this. Thank you.\r
\n" ); document.write( "\n" ); document.write( "Lorraine \n" ); document.write( "

Algebra.Com's Answer #106595 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"1%2F2+%2B+3%2Fx+=+%28x%2B6%29%2F%282x%29\"$
\n" ); document.write( "How does the x get from denominator to numerator?
\n" ); document.write( "I'm not sure how to work the problem to get the x on top.
\n" ); document.write( "Please help explain this. Thank you.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Put all the terms in parentheses:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Look at all the denominators:\r\n" );
document.write( "\r\n" );
document.write( ", and \r\n" );
document.write( "\r\n" );
document.write( "The LCD of these is , so\r\n" );
document.write( "we write  as  and\r\n" );
document.write( "multiply every term by it\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Cancel the 's in the first term on the left.\r\n" );
document.write( "Cancel the 's in the second term on the left.\r\n" );
document.write( "Cancel the 's in the term on the right:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "adding  to both sides\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This is a true numerical identity.\r\n" );
document.write( "Therefore the answer would be\r\n" );
document.write( "{all real numbers}, however we can see\r\n" );
document.write( "that x cannot be 0 since it would\r\n" );
document.write( "cause two denominators in the original\r\n" );
document.write( "equation to be 0.  Therefore any value \r\n" );
document.write( "of x except 0 is a solution.  So the\r\n" );
document.write( "solution set is graphed as:\r\n" );
document.write( "\r\n" );
document.write( "<=====================o====================>\r\n" );
document.write( " -5  -4  -3  -2  -1   0   1   2   3   4   5    \r\n" );
document.write( "\r\n" );
document.write( "or in interval notation:   (,)(,)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );