document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=547530>Question 547530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the equations of any vertical asymptotes and the values of x for any holes in the graph of each rational function.\r<BR>\n" );
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document.write( "f(x)=2x^2-x-10/(2x-5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356436 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=356436\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2-x-10%29%2F%282x-5%29 ALIGN=MIDDLE  ALT=\"%282x%5E2-x-10%29%2F%282x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B2%29%282x-5%29%29%2F%282x-5%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B2%29%282x-5%29%29%2F%282x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2x-5 must not be 0 since denominators are never 0.\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "2x - 5 &#8800; 0<BR>\n" );
document.write( "    2x &#8800; 5<BR>\n" );
document.write( "     x &#8800; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can cancel those as long as we require x &#8800; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B2%29%28cross%282x-5%29%29%29%2F%28cross%282x-5%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B2%29%28cross%282x-5%29%29%29%2F%28cross%282x-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where x &#8800; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f(x) = x+2,  x &#8800; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since x &#8800; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, f(x) &#8800; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2%2B2 ALIGN=MIDDLE  ALT=\"5%2F2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the graph is this line with a hole:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-5%2C5%2C-3%2C7%2Cgraph%28400%2C400%2C-5%2C5%2C-3%2C7%29%2C%0D%0Acircle%282.5%2C4.5%2C.1%29%2C+line%28-11%2C-9%2C2.4%2C4.4%29%2C+line%282.6%2C4.6%2C11%2C13%29%2C%0D%0Alocate%282.5%2C4.5%2CH%285%2F2%2C9%2F2%29%29%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "with a hole at the point H(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "There are no asymptotes.\r<BR>\n" );
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document.write( "Edwin</pre>       </SPAN>\n" );
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