document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252031>Question 252031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this equation: m^2+n^2     m     n<BR>\n" );
document.write( "                                   --------  + --- + ---<BR>\n" );
document.write( "                                    m^2-n^2    n-m   m+n  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183813 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, m^2-n^2 factors to (m+n)(m-n)<BR>\n" );
document.write( "In order to add or subtract, you need to get a common denominator. remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=numerator%2Fdenominator ALIGN=MIDDLE  ALT=\"numerator%2Fdenominator\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The least common multiple of these terms is (m+n)(m-n). <BR>\n" );
document.write( "multiply each term by what it is missing to have a common denominator<BR>\n" );
document.write( "the first term, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%5E2%2Bn%5E2%29%2F%28%28m-n%29%28m%2Bn%29%29 ALIGN=MIDDLE  ALT=\"%28m%5E2%2Bn%5E2%29%2F%28%28m-n%29%28m%2Bn%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not missing anything, so leave it alone.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The second term, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2F%28n-m%29 ALIGN=MIDDLE  ALT=\"m%2F%28n-m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is very close to having the m-n of the least common denominator.  In order to make it look the same though, we need to factor out a -1.  We can also switch the order of m and n so that they look the same.  We still need to multiply by (m+n), so our second term becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28m%28m%2Bn%29%29%2F%28%28m%2Bn%29%28m-n%29%29 ALIGN=MIDDLE  ALT=\"-%28m%28m%2Bn%29%29%2F%28%28m%2Bn%29%28m-n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Our third term, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2F%28m%2Bn%29 ALIGN=MIDDLE  ALT=\"n%2F%28m%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is missing an (m-n). So multiply the top and bottom by (m-n) and we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28m-n%29%29%2F%28%28m%2Bn%29%28m-n%29%29 ALIGN=MIDDLE  ALT=\"%28n%28m-n%29%29%2F%28%28m%2Bn%29%28m-n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now that we have a common denominator, we add and subtract.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%5E2%2Bn%5E2%29%2F%28%28m-n%29%28m%2Bn%29%29-%28m%28m%2Bn%29%29%2F%28%28m%2Bn%29%28m-n%29%29%2B%28n%28m-n%29%29%2F%28%28m%2Bn%29%28m-n%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%5E2%2Bn%5E2-m%28m%2Bn%29%2Bn%28m-n%29%29%2F%28%28m%2Bn%29%28m-n%29%29 ALIGN=MIDDLE  ALT=\"%28m%5E2%2Bn%5E2-m%28m%2Bn%29%2Bn%28m-n%29%29%2F%28%28m%2Bn%29%28m-n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "distribute the -m and n<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%5E2%2Bn%5E2-m%5E2-mn%2Bmn-n%5E2%29%2F%28%28m%2Bn%29%28m-n%29%29 ALIGN=MIDDLE  ALT=\"%28m%5E2%2Bn%5E2-m%5E2-mn%2Bmn-n%5E2%29%2F%28%28m%2Bn%29%28m-n%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F%28%28m%2Bn%29%28m-n%29%29=0 ALIGN=MIDDLE  ALT=\"0%2F%28%28m%2Bn%29%28m-n%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Justin<BR>\n" );
document.write( "justin.sheppard.tech@hotmail.com\r<BR>\n" );
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