document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=295503>Question 295503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the rational funxtion f(x)=x^2+5x-6/x^2+2x-3. indentify the vertical and horizontal asymptotes, and any holes in the graph </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #213103 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=213103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplify first. <BR>\n" );
document.write( "You can factor numerator and denominator and get rid of common factors, if there are any.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x-6=%28x%2B6%29%28x-1%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x-6=%28x%2B6%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-3=%28x%2B3%29%28x-1%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-3=%28x%2B3%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B5x-6%29%2F%28x%5E2%2B2x-3%29=%28%28x%2B6%29cross%28x-1%29%29%2F%28%28x%2B3%29cross%28x-1%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=%28x%5E2%2B5x-6%29%2F%28x%5E2%2B2x-3%29=%28x%2B6%29%2F%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B5x-6%29%2F%28x%5E2%2B2x-3%29=%28x%2B6%29%2F%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Vertical asymptotes occur when the denominator goes to zero. <BR>\n" );
document.write( "For f(x), the denominator goes to zero when,<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( "To find horizontal asymptotes, divide numerator and denominator by the highest exponent x term, then take the limit.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2%2B5x-6%29%2F%28x%5E2%2B2x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B5x-6%29%2F%28x%5E2%2B2x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2%2Fx%5E2%2B5x%2Fx%5E2-6%2Fx%5E2%29%2F%28x%5E2%2Fx%5E2%2B2x%2Fx%5E2-3%2Fx%5E2%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=f%28x%29=%281%2B5%2Fx-6%2Fx%5E2%29%2F%281%2B2%2Fx-3%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%281%2B5%2Fx-6%2Fx%5E2%29%2F%281%2B2%2Fx-3%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in the limit, the crossed out terms go to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%281%2Bcross%285%2Fx%29-cross%286%2Fx%5E2%29%29%2F%281%2Bcross%282%2Fx%29-cross%283%2Fx%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3Einfinity%2C+f%28x%29%29=1 ALIGN=MIDDLE  ALT=\"lim%28x-%3Einfinity%2C+f%28x%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There is a horizontal asymptote at <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;\" >.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since there is a division by zero at <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;\" >, the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29 ALIGN=MIDDLE  ALT=\"f%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is undefined. <BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-10%2C+10%2C+-5%2C+5%2Cgreen%28line%28-3%2C-10%2C-3%2C10%29%29%2Cblue%28line%28-20%2C1%2C20%2C1%29%29%2C%0D%0A+graph%28+300%2C+300%2C+-10%2C+10%2C+-5%2C+5%2C+%28x%5E2%2B5x-6%29%2F%28x%5E2%2B2x-3%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );