document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125161>Question 1125161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> where does the rational function <BR>\n" );
document.write( "f(x)=7 (x+54)(x-40)/(x+56)(x+87)(x-55)<BR>\n" );
document.write( "holes and vertical asymptotes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741480 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=741480\">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=%287+%28x%2B54%29%28x-40%29%29%2F%28%28x%2B56%29%28x%2B87%29%28x-55%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%287+%28x%2B54%29%28x-40%29%29%2F%28%28x%2B56%29%28x%2B87%29%28x-55%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "holes: <BR>\n" );
document.write( "To find the holes in a rational function, you must factor the numerator and denominator of the rational function and see if there are any common factors, then simplify it. If there is the same factor in  the numerator and denominator, there is a hole.\r<BR>\n" );
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document.write( "you are given<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%287+%28x%2B54%29%28x-40%29%29%2F%28%28x%2B56%29%28x%2B87%29%28x-55%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%287+%28x%2B54%29%28x-40%29%29%2F%28%28x%2B56%29%28x%2B87%29%28x-55%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is already factored and you can see there is nothing to simplify,  there are no common factors, means there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no+ ALIGN=MIDDLE  ALT=\"no+\"   DISABLED_style= \"max-width:90%; height:auto;\" >holes\r<BR>\n" );
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document.write( "and vertical asymptotes:\r<BR>\n" );
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document.write( "I'll find any vertical asymptotes, by setting the denominator equal to zero and solving:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B56%29%28x%2B87%29%28x-55%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B56%29%28x%2B87%29%28x-55%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and it is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B56%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B56%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-56 ALIGN=MIDDLE  ALT=\"x=-56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B87%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B87%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-87 ALIGN=MIDDLE  ALT=\"x=-87\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-55%29=0 ALIGN=MIDDLE  ALT=\"%28x-55%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=55 ALIGN=MIDDLE  ALT=\"x=55\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a vertical asymptotes are at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-56 ALIGN=MIDDLE  ALT=\"x=-56\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-87 ALIGN=MIDDLE  ALT=\"x=-87\"   DISABLED_style= \"max-width:90%; height:auto;\" >,and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=55 ALIGN=MIDDLE  ALT=\"x=55\"   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+-130%2C+130%2C+-10%2C10%2C%0D%0Aline%28-56%2C10%2C-56%2C-10%29%2Cline%28-87%2C10%2C-87%2C-10%29%2Cline%2855%2C10%2C55%2C-10%29%2C%0D%0A+graph%28+600%2C+600%2C+-130%2C+130%2C+-10%2C10%2C%287+%28x%2B54%29%28x-40%29%29%2F%28%28x%2B56%29%28x%2B87%29%28x-55%29%29%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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