document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132097>Question 1132097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many ordered pairs of positive integers (x,y) satisfy the equation x=(4-x)/(y^2-x)? \r<BR>\n" );
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document.write( "My work: I am pretty sure that the only possible pair is (1,2), but I don’t know how to mathematically explain it... I just need help on this process.<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 #748984 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "you are right, it is  ordered pair (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "explanation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284-x%29%2F%28y%5E2-x%29 ALIGN=MIDDLE  ALT=\"x=%284-x%29%2F%28y%5E2-x%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=x%28y%5E2-x%29=%284-x%29 ALIGN=MIDDLE  ALT=\"x%28y%5E2-x%29=%284-x%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=%28y%5E2-x%29=%284-x%29%2Fx ALIGN=MIDDLE  ALT=\"%28y%5E2-x%29=%284-x%29%2Fx\"   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%5E2-x=%284-x%29%2Fx ALIGN=MIDDLE  ALT=\"y%5E2-x=%284-x%29%2Fx\"   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%5E2=%284-x%29%2Fx%2Bx ALIGN=MIDDLE  ALT=\"y%5E2=%284-x%29%2Fx%2Bx\"   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%5E2=%284-x%29%2Fx%2Bx%5E2%2Fx ALIGN=MIDDLE  ALT=\"y%5E2=%284-x%29%2Fx%2Bx%5E2%2Fx\"   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%5E2=%28x%5E2-x%2B4%29%2Fx ALIGN=MIDDLE  ALT=\"y%5E2=%28x%5E2-x%2B4%29%2Fx\"   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=sqrt%28%28x%5E2-x%2B4%29%2Fx%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28%28x%5E2-x%2B4%29%2Fx%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=y=sqrt%28x%5E2-x%2B4%29%2Fsqrt%28x%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28x%5E2-x%2B4%29%2Fsqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4%3C%3E0 ALIGN=MIDDLE  ALT=\"x-4%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, lowest integer we can choose for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1 ALIGN=MIDDLE  ALT=\"+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%281%5E2-1%2B4%29%2Fsqrt%281%29 ALIGN=MIDDLE  ALT=\"y=sqrt%281%5E2-1%2B4%29%2Fsqrt%281%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=y=sqrt%284%29%2F1 ALIGN=MIDDLE  ALT=\"y=sqrt%284%29%2F1\"   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+ ALIGN=MIDDLE  ALT=\"y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2 ALIGN=MIDDLE  ALT=\"+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>since we need  ordered pairs of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive ALIGN=MIDDLE  ALT=\"positive\"   DISABLED_style= \"max-width:90%; height:auto;\" > integers, we will use only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, we have one ordered pair of positive integers (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >) satisfy the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284-x%29%2F%28y%5E2-x%29 ALIGN=MIDDLE  ALT=\"x=%284-x%29%2F%28y%5E2-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it is  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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