document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=375997>Question 375997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to find the answer to this, and I'm having a lot of problems.\r<BR>\n" );
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document.write( "((3x+1)/(9x^2-1)) - ((2)/3x-1)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #267426 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=267426\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ((3x+1)/(9x^2-1)) - ((2)/3x-1))<BR>\n" );
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document.write( "Notice that<BR>\n" );
document.write( "(9x^2-1)<BR>\n" );
document.write( "can be written as a \"difference of squares\":<BR>\n" );
document.write( "((3x)^2-1^2)<BR>\n" );
document.write( "which can be factored as:<BR>\n" );
document.write( "(3x-1)(3x+1)<BR>\n" );
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document.write( "So,we can rewrite:<BR>\n" );
document.write( "((3x+1)/(9x^2-1)) - ((2)/3x-1))<BR>\n" );
document.write( "as<BR>\n" );
document.write( "((3x+1)/((3x-1)(3x+1))) - ((2)/3x-1))<BR>\n" );
document.write( "canceling like-terms:<BR>\n" );
document.write( "(1/(3x-1)) - ((2)/3x-1))<BR>\n" );
document.write( "Now we can combine as:\r<BR>\n" );
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document.write( "(1-2)/(3x-1)\r<BR>\n" );
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document.write( "-1/(3x-1)<BR>\n" );
document.write( "or<BR>\n" );
document.write( "1/(1-3x)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );