document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887756>Question 887756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the graph of the rational function? \r<BR>\n" );
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document.write( "y= x^2-7x+12/x^2-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536856 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=536856\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The graph of y= x^2-7x+12/x^2-1 is this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-25%2C25%2C-15%2C40%2Cx%5E2-7x%2B12%2Fx%5E2-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-25%2C25%2C-15%2C40%2Cx%5E2-7x%2B12%2Fx%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But that is not what you want.\r<BR>\n" );
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document.write( "You want this:<BR>\n" );
document.write( "y= (x^2-7x+12)/(x^2-1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+%28x%5E2-7x%2B12%29%2F%28x%5E2-1%29 ALIGN=MIDDLE  ALT=\"y=+%28x%5E2-7x%2B12%29%2F%28x%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That seems not factorable to simplify, but there is still some information to learn about the graph if factor the function.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28x-3%29%28x-4%29%29%2F%28%28x-1%29%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"y=%28%28x-3%29%28x-4%29%29%2F%28%28x-1%29%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Zeros at x=3 and x=4.<BR>\n" );
document.write( "Asymtptotes (vertical) at x=1 and x=-1.<BR>\n" );
document.write( "You can test the intervals around all critical points...\r<BR>\n" );
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document.write( "THIS is the graph. (Difficult for this to appear well on the system)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-15%2C15%2C-15%2C15%2C%28x%5E2-7x%2B12%29%2F%28x%5E2-1%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-15%2C15%2C-15%2C15%2C%28x%5E2-7x%2B12%29%2F%28x%5E2-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A zoom-in on the right side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C2%2C5%2C-1%2C1%2C%28x%5E2-7x%2B12%29%2F%28x%5E2-1%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C2%2C5%2C-1%2C1%2C%28x%5E2-7x%2B12%29%2F%28x%5E2-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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