document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162413>Question 162413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to simplify 2 fraction problems with variables and exponents, probably using factoring, but depite all the factoring I have tried, my answers don't come up with common denominators, so the numbers don't combine.  Here is the first problem:\r<BR>\n" );
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document.write( "yx^2/(x-y)+xy^3/(xy-x^2)\r<BR>\n" );
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document.write( "This is the second:\r<BR>\n" );
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document.write( "1/(a^2+b^2)+1/(a^2-b^2)+2b^2/(a^4-b^4)\r<BR>\n" );
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document.write( "Any help you can give would be REALLY awesome!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119697 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=119697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is the first problem: <BR>\n" );
document.write( "yx^2/(x-y)+xy^3/(xy-x^2)\r<BR>\n" );
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document.write( "= yx^2/(x-y)+xy^3/(-x(x-y))\r<BR>\n" );
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document.write( "The LCD = -x(x-y)\r<BR>\n" );
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document.write( "= -yx^3/lcd + xy^3/lcd\r<BR>\n" );
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document.write( "= [-yx^3 + xy^3]/lcd\r<BR>\n" );
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document.write( "= [-xy(x^2 - y^2)]/[-x(x-y)]\r<BR>\n" );
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document.write( "= [y(x + y)]<BR>\n" );
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document.write( "This is the second: <BR>\n" );
document.write( "1/(a^2+b^2) + 1/(a^2-b^2) + 2b^2/(a^4-b^4) \r<BR>\n" );
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document.write( "lcd = a^4 - b^4<BR>\n" );
document.write( "-----------------------\r<BR>\n" );
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document.write( "= (a^2 - b^2)/lcd + (a^2 + b^2)/lcd + 2b^2/lcd\r<BR>\n" );
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document.write( "Add the three numerators to get:\r<BR>\n" );
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document.write( "= (2a^2 + 2b^2)/lcd\r<BR>\n" );
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document.write( "= [2(a^2+b^2)] / [(a^2+b^2)(a^2-b^2)]\r<BR>\n" );
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document.write( "= 2/(a^2-b^2)<BR>\n" );
document.write( "==========================================\r<BR>\n" );
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document.write( "Chers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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