document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101554>Question 1101554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a rational function has poles at x=1<BR>\n" );
document.write( "x<BR>\n" );
document.write( "=<BR>\n" );
document.write( "1<BR>\n" );
document.write( " and x=2<BR>\n" );
document.write( "x<BR>\n" );
document.write( "=<BR>\n" );
document.write( "2<BR>\n" );
document.write( ", zeros at x=4<BR>\n" );
document.write( "x<BR>\n" );
document.write( "=<BR>\n" );
document.write( "4<BR>\n" );
document.write( " and x=5<BR>\n" );
document.write( "x<BR>\n" );
document.write( "=<BR>\n" );
document.write( "5<BR>\n" );
document.write( ", and a horizontal asymptote y=3<BR>\n" );
document.write( "y<BR>\n" );
document.write( "=<BR>\n" );
document.write( "3<BR>\n" );
document.write( ". Find a possible rational function that has the attributes listed above. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716187 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "To have a pole at x=a, the denominator of the rational function must contain a factor of (x-a).<br><BR>\n" );
document.write( "In your example, with poles at x=1 and x=2, we need factors of (x-1) and (x-2) in the denominator.<br><BR>\n" );
document.write( "To get a zero at x=b, the numerator of the rational function must contain a factor of (x-b).<br><BR>\n" );
document.write( "In your example, with zeros at x=4 and x=5, we need factors of (x-4) and (x-5) in the numerator.<br><BR>\n" );
document.write( "To get a horizontal asymptote of y=3, we need the degrees of the numerator and denominator to be the same, and we need the leading coefficient in the numerator to be 3 times the leading coefficient in the denominator.<br><BR>\n" );
document.write( "The simplest rational function that satisfies all these requirements is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%28x-4%29%28x-5%29%29%2F%28x-1%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%28%283%28x-4%29%28x-5%29%29%2F%28x-1%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );