document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185459>Question 185459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show by counterexample that (x+y)^-2 and x^-2+y^-2 are not equivalent. please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139133 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=139133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Proof by Counterexample: \r<BR>\n" );
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document.write( "Simply pick two random values for \"x\" and \"y\" and plug them in. I'm going to use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these values are small and nonzero)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E%28-2%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B1%29%5E%28-2%29 ALIGN=MIDDLE  ALT=\"%281%2B1%29%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   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=%282%29%5E%28-2%29 ALIGN=MIDDLE  ALT=\"%282%29%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282%5E2%29 ALIGN=MIDDLE  ALT=\"1%2F%282%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the fraction (to make the exponent positive)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E%28-2%29=1%2F4 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E%28-2%29=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "----------------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-2%29%2By%5E%28-2%29 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29%2By%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the second expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E%28-2%29%2B1%5E%28-2%29 ALIGN=MIDDLE  ALT=\"1%5E%28-2%29%2B1%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: these values cannot change now)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1%5E2%2B1%2F1%5E2 ALIGN=MIDDLE  ALT=\"1%2F1%5E2%2B1%2F1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the fractions (to make the exponents positive)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1%2B1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1%2B1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 1 to get 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B1 ALIGN=MIDDLE  ALT=\"1%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-2%29%2By%5E%28-2%29=2 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29%2By%5E%28-2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "----------------------------------------------\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E%28-2%29=1%2F4 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E%28-2%29=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-2%29%2By%5E%28-2%29=2 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29%2By%5E%28-2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E%28-2%29%3C%3Ex%5E%28-2%29%2By%5E%28-2%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E%28-2%29%3C%3Ex%5E%28-2%29%2By%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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