document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239400>Question 239400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having a hard time understanding this kind of problem....I'll try to type it out as best as I can.  Any help would be appreciated.  Thank you..\r<BR>\n" );
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document.write( "Complex Rational Expressions...\r<BR>\n" );
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document.write( "Simplify<BR>\n" );
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document.write( "[x+1/x-1 + 1]^5<BR>\n" );
document.write( "_______________     <BR>\n" );
document.write( "[x+1/x-1 - 1] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175752 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175752\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "You really need to use parentheses more because I am having to guess at what you mean.\r<BR>\n" );
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document.write( "I think you are trying to represent\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\left(\frac{x+1}{x-1}\ +\  1\right)^5}{\left(\frac{x+1}{x-1}\ -\ 1\right)}\">\r<BR>\n" );
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document.write( "If this is correct, you should have represented it as:\r<BR>\n" );
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document.write( "[((x+1)/(x-1)) + 1]^5<BR>\n" );
document.write( "_______________     <BR>\n" );
document.write( "[((x+1)/(x-1)) - 1]\r<BR>\n" );
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document.write( "Continuing on that presumption, begin with the numerator.  The LCD in the numerator is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ 1\">, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\left(\frac{x+1+(x-1)}{x-1}\right)^5}{\left(\frac{x+1}{x-1}\ -\ 1\right)}\">\r<BR>\n" );
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document.write( "The LCD in the denominator is also <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ 1\">, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\left(\frac{x+1+(x-1)}{x-1}\right)^5}{\left(\frac{x+1-(x-1)}{x-1}\right)}\">\r<BR>\n" );
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document.write( "Collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\left(\frac{2x}{x-1}\right)^5}{\left(\frac{2}{x-1}\right)}\">\r<BR>\n" );
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document.write( "Factor <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^5\"> from the numerator of the numerator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\left(\frac{2}{x-1}\right)^5}{\left(\frac{2}{x-1}\right)}x^5\">\r<BR>\n" );
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document.write( "Use\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{a^m}{a^n}\ =\ a^{m-n}\">\r<BR>\n" );
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document.write( "to write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{2}{x-1}\right)^4\,x^5\">\r<BR>\n" );
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document.write( "There are a couple of different ways to go from here.  If this were an intermediate calculation, I would leave it like it is since this expression is probably easier to manipulate than any expanded version.  But you can easily expand it if you like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{16x^5}{(x-1)^4}\">\r<BR>\n" );
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document.write( "Or go one step further and use the Binomial Theorem to expand the denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{16x^5}{x^4-4x^3+6x^2-4x+1}\">\r<BR>\n" );
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document.write( "Which is 'simplest' becomes a matter of artistic license at this point.  Your choice.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
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