document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87795>Question 87795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve the following equation:<BR>\n" );
document.write( "Peform the indicated operation.\r<BR>\n" );
document.write( "\n" );
document.write( "x^3-1/x^2+1 divided by 9x^2+9x+9/x^2-x\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you very much!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63687 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=63687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28x%5E3-1%29%2F%28x%5E2%2B1%29+%29+%2F+%28+%289x%5E2%2B9x%2B9%29%2F%28x%5E2-x%29+%29+ ALIGN=MIDDLE  ALT=\"+%28+%28x%5E3-1%29%2F%28x%5E2%2B1%29+%29+%2F+%28+%289x%5E2%2B9x%2B9%29%2F%28x%5E2-x%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28x%5E3-1%29%2F%28x%5E2%2B1%29+%29+%2A+%28+%28x%5E2-x%29%2F%289x%5E2%2B9x%2B9%29+%29+ ALIGN=MIDDLE  ALT=\"+%28+%28x%5E3-1%29%2F%28x%5E2%2B1%29+%29+%2A+%28+%28x%5E2-x%29%2F%289x%5E2%2B9x%2B9%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28x%5E3-1%29%2F%28x%5E2%2B1%29+%29+%2A+%28+%28x%28x-1%29%29%2F%289%28x%5E2%2Bx%2B1%29%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28x%28x-1%29%28x%5E3-1%29%29+%29+%2F+%28+%289%28x%5E2%2Bx%2B1%29%28x%5E2%2B1%29%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now - i know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E3-1 ALIGN=MIDDLE  ALT=\"+x%5E3-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > factorises to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-1%29%28x%5E2%2Bx%2B1%29+ ALIGN=MIDDLE  ALT=\"+%28x-1%29%28x%5E2%2Bx%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can write\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28x%28x-1%29%28x-1%29%28x%5E2%2Bx%2B1%29%29+%29+%2F+%28+%289%28x%5E2%2Bx%2B1%29%28x%5E2%2B1%29%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and now we can cancel some terms down<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28x%28x-1%29%28x-1%29%29+%29+%2F+%28+%289%28x%5E2%2B1%29%29+%29+ ALIGN=MIDDLE  ALT=\"+%28+%28x%28x-1%29%28x-1%29%29+%29+%2F+%28+%289%28x%5E2%2B1%29%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28x%28x-1%29%5E2%29+%29+%2F+%28+%289%28x%5E2%2B1%29%29+%29+ ALIGN=MIDDLE  ALT=\"+%28+%28x%28x-1%29%5E2%29+%29+%2F+%28+%289%28x%5E2%2B1%29%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is as far as we can go with just real numbers - the quadratic does simplify but you need to know some Complex Numbers: its final version is\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+%28x%28x-1%29%28x-1%29%29+%29+%2F+%28+%289%28x%2Bi%29%28x-i%29%29+%29+ ALIGN=MIDDLE  ALT=\"+%28+%28x%28x-1%29%28x-1%29%29+%29+%2F+%28+%289%28x%2Bi%29%28x-i%29%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where the denominator has \"i\" and not a 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cheers<BR>\n" );
document.write( "jon<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );