document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190296>Question 190296</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi.\r<BR>\n" );
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document.write( "I need some help reducing this rational expression completely:\r<BR>\n" );
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document.write( "n^3 - 1/n^2 - 1\r<BR>\n" );
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document.write( "thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142819 by </B><A HREF=/tutors/aboutme.mpl?userid=feliz1965><B>feliz1965(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=feliz1965><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=142819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the numerator, we have the difference of two cubes.\r<BR>\n" );
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document.write( "a^3 – b^3 = (a – b)(a^2 + ab + b^2)\r<BR>\n" );
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document.write( "Let a = n\r<BR>\n" );
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document.write( "Using this rule, the numerator becomes \r<BR>\n" );
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document.write( "n^3 - 1 = (n - 1)(n^2 + n(-1) + (-1)^2)\r<BR>\n" );
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document.write( "n^3 - 1 = (n - 1)(n^2 - n + 1)\r<BR>\n" );
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document.write( "The denominator is the difference of two perfect squares.\r<BR>\n" );
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document.write( "n^2 - 1 = (n - 1)(n + 1)\r<BR>\n" );
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document.write( "We now have this fraction:\r<BR>\n" );
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document.write( "[(n - 1)(n^2 - n + 1)]/(n - 1)(n + 1)\r<BR>\n" );
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document.write( "We can cancel like terms located in the numerator and denominator.\r<BR>\n" );
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document.write( "In this question, that means removing (n - 1).\r<BR>\n" );
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document.write( "Final answer: (n^2 - n + 1)]/(n + 1)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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