document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=9727>Question 9727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If P=x+1/x-1 and Q=x-1/x+1, find P^2+Q^2-PQ. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5258 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=5258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  First of all, alway remember to put parentheses to group related terms,<BR>\n" );
document.write( " as P= (x+1)/(x-1) and Q=(x-1)/(x+1).\r<BR>\n" );
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document.write( " Note, P = 1 + [2/(x-1)] and  Q = 1/P = 1 + [-2/(x+1)] <BR>\n" );
document.write( " So,P-Q = 2[1/(x-1) + 1/(x+1)] = 2[2x/(x^2-1)]<BR>\n" );
document.write( "   =  4x/(x^2-1) <BR>\n" );
document.write( " and PQ = ??(for you)\r<BR>\n" );
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document.write( " Since P^2+Q^2-PQ  = (P-Q)^2 +PQ (why ?)<BR>\n" );
document.write( " We have P^2+Q^2-PQ  = [4x/(x^2-1)]^2 + 1<BR>\n" );
document.write( "  = 1 + 16x^2 /(x^2-1)^2 \r<BR>\n" );
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document.write( " Of course ,you can use direct substitution and staightford computation<BR>\n" );
document.write( " to get the same asnwer. But, the above way it faster and can avoid some<BR>\n" );
document.write( " mistakes.<BR>\n" );
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document.write( " I won't give further explanations for this level of questions.\r<BR>\n" );
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document.write( " Kenny<BR>\n" );
document.write( "  </SPAN>\n" );
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