document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=732048>Question 732048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to find the slant asymptote of the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=%28-4%2Ax%5E2%2B6%2Ax%2B3%29%2F%286%2Ax%2B9%29 ALIGN=MIDDLE  ALT=\"+f%28x%29=%28-4%2Ax%5E2%2B6%2Ax%2B3%29%2F%286%2Ax%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #447462 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=447462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Oblique or Slant Asymptote\r<BR>\n" );
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document.write( "An oblique or a slant asymptote is an asymptote<BR>\n" );
document.write( "that is neither vertical or horizontal.\r<BR>\n" );
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document.write( "If the degree of the numerator is one more than<BR>\n" );
document.write( "the degree of the denominator, then the graph of<BR>\n" );
document.write( "the rational function will have a slant asymptote.\r<BR>\n" );
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document.write( "The slant asymptote is the quotient part of the answer you get when you divide the numerator by the denominator.You may have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > slant asymptote,  but no more than that.\r<BR>\n" );
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document.write( "You draw a slant asymptote on the graph by putting a dashed horizontal (left and right) line going through <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Applying long division to this problem we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28-4x%5E2%2B6x%2B3%29%2F%286x%2B9%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28-4x%5E2%2B6x%2B3%29%2F%286x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "..................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%2F3%2B2 ALIGN=MIDDLE  ALT=\"-2x%2F3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B9 ALIGN=MIDDLE  ALT=\"6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >)|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B6x%2B3 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B6x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B6x ALIGN=MIDDLE  ALT=\"-4x%5E2%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "________________________<BR>\n" );
document.write( ".....................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B3 ALIGN=MIDDLE  ALT=\"12x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".....................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B18 ALIGN=MIDDLE  ALT=\"12x%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15 ALIGN=MIDDLE  ALT=\"-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282%2F3%29x%2B2+-15%2F%286x%2B9%29 ALIGN=MIDDLE  ALT=\"-%282%2F3%29x%2B2+-15%2F%286x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The equation for the slant asymptote is the quotient part of the answer which would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%282%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y=-%282%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find two points and draw the slant asymptote:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%282%2F3%29x%2B2%2C+%28-4x%5E2%2B6x%2B3%29%2F%286x%2B9%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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