document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=892661>Question 892661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me out with this question:<BR>\n" );
document.write( "How to find the oblique or curvilinear asymptotes for this function<BR>\n" );
document.write( ".   f(X)= (X^3-1)/(x^2-9)<BR>\n" );
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 #540691 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=540691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Perform the polynomial division.  You should likely find a remainder, which may become increasingly small as x tends to plus or minus infinity, meaning that the quotient without the remainder will be the slant asymptote.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You have a rational expression function.  Divide <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;\" >  by  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-9 ALIGN=MIDDLE  ALT=\"x%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  <BR>\n" );
document.write( "The quotient found is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%2B%289x-1%29%2F%28x%5E2-9%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%2B%289x-1%29%2F%28x%5E2-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Notice the degree of the numerator of the remainder is smaller than the degree of the denominator of the remainder.  As x goes to either extreme, the quotient gets closer to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=x%29 ALIGN=MIDDLE  ALT=\"highlight%28y=x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the slant asymptote.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Compare with the graph:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-15%2C15%2C-15%2C15%2C%28x%5E3-1%29%2F%28x%5E2-9%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-15%2C15%2C-15%2C15%2C%28x%5E3-1%29%2F%28x%5E2-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ",and then showing the included line for the asymptote,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-15%2C15%2C-15%2C15%2C%28x%5E3-1%29%2F%28x%5E2-9%29%2Cx%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-15%2C15%2C-15%2C15%2C%28x%5E3-1%29%2F%28x%5E2-9%29%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );