document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1048379>Question 1048379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For all positive integers x and y such that 1/x + 1/y = 1/12, find the greatest value that y can have.\r<BR>\n" );
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document.write( "What is the way to do this? Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #663949 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=663949\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do you need a specific way of dealing with this, or is making a graph acceptable and looking for integer points?\r<BR>\n" );
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document.write( "12xy is common denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12xy%281%2Fx%2B1%2Fy%29=12xy%281%2F12%29 ALIGN=MIDDLE  ALT=\"12xy%281%2Fx%2B1%2Fy%29=12xy%281%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y%2B12x=xy ALIGN=MIDDLE  ALT=\"12y%2B12x=xy\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy-12y=12x ALIGN=MIDDLE  ALT=\"xy-12y=12x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28x-12%29=12x ALIGN=MIDDLE  ALT=\"y%28x-12%29=12x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2812x%29%2F%28x-12%29 ALIGN=MIDDLE  ALT=\"y=%2812x%29%2F%28x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but does this have a maximum?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%28%28x-12%29%2A12-12x%2A1%29%2F%28x-12%29%5E2 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%28%28x-12%29%2A12-12x%2A1%29%2F%28x-12%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, derivative, Quotient Rule.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=%2812x-144-12x%29%2F%28x-12%29%5E2 ALIGN=MIDDLE  ALT=\"dy%2Fdx=%2812x-144-12x%29%2F%28x-12%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=-144%2F%28x-12%29%5E2 ALIGN=MIDDLE  ALT=\"dy%2Fdx=-144%2F%28x-12%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >------THIS IS NEVER 0.<BR>\n" );
document.write( "But you are looking for POSITIVE integers.\r<BR>\n" );
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document.write( "You could try positive integers x starting with 0, on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2812x%29%2F%28x-12%29 ALIGN=MIDDLE  ALT=\"y=%2812x%29%2F%28x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Would any acceptable y, integer, also be positive?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-8%2C8%2C-8%2C8%2C12x%2F%28x-12%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-8%2C8%2C-8%2C8%2C12x%2F%28x-12%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<b>NO.</b> </SPAN>\n" );
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