document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92456>Question 92456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please show me in detail this problem:\r<BR>\n" );
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document.write( "1/x + 6/y<BR>\n" );
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document.write( "1/x2 - 36/y2\r<BR>\n" );
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document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67362 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=67362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Could you please show me in detail this problem: <BR>\n" );
document.write( "1/x + 6/y<BR>\n" );
document.write( "___________ <BR>\n" );
document.write( "1/x2 - 36/y2 <BR>\n" );
document.write( "Thank you very much!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Fx%29%2B%286%2Fy%29%29%2F%28%281%2Fx%5E2%29-%2836%2Fy%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2Fx%29%2B%286%2Fy%29%29%2F%28%281%2Fx%5E2%29-%2836%2Fy%5E2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Our approach will be to first simplify the numerator and then simplify the denominator and finally put them back together and simplify again.\r<BR>\n" );
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document.write( "Numerator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%29%2B%286%2Fy%29 ALIGN=MIDDLE  ALT=\"%281%2Fx%29%2B%286%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  multiply each term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2Fxy ALIGN=MIDDLE  ALT=\"xy%2Fxy\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B6x%29%2Fxy ALIGN=MIDDLE  ALT=\"%28y%2B6x%29%2Fxy\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next the denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%5E2%29-%2836%2Fy%5E2%29 ALIGN=MIDDLE  ALT=\"%281%2Fx%5E2%29-%2836%2Fy%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiply each term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2y%5E2%2Fx%5E2y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2y%5E2%2Fx%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2-36x%5E2%29%2Fx%5E2y%5E2 ALIGN=MIDDLE  ALT=\"%28y%5E2-36x%5E2%29%2Fx%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we can further simplify this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-6x%29%28y%2B6x%29%29%2Fx%5E2y%5E2 ALIGN=MIDDLE  ALT=\"%28%28y-6x%29%28y%2B6x%29%29%2Fx%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  now we can put the numerator and denominator back together\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%2B6x%29%2Fxy%29%2F%28%28%28y-6x%29%28y%2B6x%29%29%2Fx%5E2y%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28y%2B6x%29%2Fxy%29%2F%28%28%28y-6x%29%28y%2B6x%29%29%2Fx%5E2y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  We will now multiply the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2y%5E2%2F%28%28y-6x%29%28y%2B6x%29%29 ALIGN=MIDDLE  ALT=\"x%5E2y%5E2%2F%28%28y-6x%29%28y%2B6x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  By doing this, our denominator will become 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28y%2B6x%29%2Fxy%29%2A%28x%5E2y%5E2%2F%28%28y-6x%29%28y%2B6x%29%29%29%29%2F%28%28%28%28y-6x%29%28y%2B6x%29%29%2Fx%5E2y%5E2%29%2A%28x%5E2y%5E2%2F%28%28y-6x%29%28y%2B6x%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  Now when we start simplifying this expression we end up with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xy%2F%28y-6x%29%29%2F1 ALIGN=MIDDLE  ALT=\"%28xy%2F%28y-6x%29%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this equals:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2F%28y-6x%29 ALIGN=MIDDLE  ALT=\"xy%2F%28y-6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------------------ans\r<BR>\n" );
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document.write( "Hope this helps----ptaylor<BR>\n" );
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