document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197629>Question 1197629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the vertical and a horizontal asymptote at y, if any, for the function f(x)=x^2+x-30 / x^2-2x-15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830983 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=830983\">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=f%28x%29=%28x%5E2%2Bx-30+%29%2F+%28x%5E2-2x-15%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2Bx-30+%29%2F+%28x%5E2-2x-15%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=f%28x%29=%28%28x+%2B+6%29+%28x+-+5%29+%29%2F+%28%28x+%2B+3%29+%28x+-+5%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28%28x+%2B+6%29+%28x+-+5%29+%29%2F+%28%28x+%2B+3%29+%28x+-+5%29%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=f%28x%29=%28x+%2B+6+%29%2F+%28x+%2B+3%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=%28x+%2B+6+%29%2F+%28x+%2B+3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Vertical asymptote : \r<BR>\n" );
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document.write( "To find the vertical asymptote of a rational function, we simplify it first to lowest terms, set its <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=denominator ALIGN=MIDDLE  ALT=\"denominator\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+equal+ ALIGN=MIDDLE  ALT=\"+equal+\"   DISABLED_style= \"max-width:90%; height:auto;\" >to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+zero ALIGN=MIDDLE  ALT=\"+zero\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and then solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > values.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+3%29=0 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( " the vertical asymptote is <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;\" >\r<BR>\n" );
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document.write( "The method to find the horizontal asymptote changes based on the degrees of the polynomials in the numerator and denominator of the function.\r<BR>\n" );
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document.write( "If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote!\r<BR>\n" );
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document.write( "in your case the polynomials have the  degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   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=y=1%2F1=1 ALIGN=MIDDLE  ALT=\"y=1%2F1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Horizontal asymptote is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   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=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%0D%0Agreen%28line%28-3%2C10%2C-3%2C-10%29%29%2Cgreen%28line%28-10%2C1%2C10%2C1%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%5E2%2Bx-30+%29%2F+%28x%5E2-2x-15%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( " </SPAN>\n" );
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