document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=719218>Question 719218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-%28x-1%29%5E2%282-x%29%29%2F%28%283-x%29%285x-1%29%5E2%29%3E=0+ ALIGN=MIDDLE  ALT=\"+%28-%28x-1%29%5E2%282-x%29%29%2F%28%283-x%29%285x-1%29%5E2%29%3E=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It would be very nice to have explanations too.<BR>\n" );
document.write( "Thanks,<BR>\n" );
document.write( "Richard </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #441258 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=441258\">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=+%28-%28x-1%29%5E2%282-x%29%29%2F%28%283-x%29%285x-1%29%5E2%29%3E=0+ ALIGN=MIDDLE  ALT=\"+%28-%28x-1%29%5E2%282-x%29%29%2F%28%283-x%29%285x-1%29%5E2%29%3E=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "critical points:<BR>\n" );
document.write( "x=1 (multiplicity 2)<BR>\n" );
document.write( "x=2<BR>\n" );
document.write( "x=3<BR>\n" );
document.write( "x=1/5 (multiplicity 2)<BR>\n" );
document.write( "Draw a number line with critical points on it:<BR>\n" );
document.write( "<....-...1/5...-....1....-.....2...+.....3.....-.....><BR>\n" );
document.write( "Explanation:<BR>\n" );
document.write( "When x>3, the expression becomes positive, but the negative sign in front makes it negative instead.<BR>\n" );
document.write( "Going thru each critical point to the left, the intervals switch signs for odd multiplicities like 1,3, etc, but do not switch when going thru even multiplicities like 2,4, etc.<BR>\n" );
document.write( "Solution: [2,3] (this is the only interval where x-values make the expression &#8805;0)<BR>\n" );
document.write( "You could also do this with a chart but is is a much longer and tedious process.<BR>\n" );
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