document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190872>Question 1190872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the gradient of the curve y = x + 4/(x-5) at the points where the curve crosses the x-axis </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822651 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=0, then x=-4/(x-5)<BR>\n" );
document.write( "x^2-5x=-4 multiplying through<BR>\n" );
document.write( "x^2-5x+4=0<BR>\n" );
document.write( "(x-4)(x-1)=0<BR>\n" );
document.write( "x=4 and 1, so looking at (1, 0) and (4, 0)<BR>\n" );
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document.write( "take the derivative:<BR>\n" );
document.write( "y'=1-4/(x-5)^2<BR>\n" );
document.write( "=1-[4/(x-5)^2]. When x=1 y'=1-(1/4) so slope is (3/4);when x=4 y'=-3\r<BR>\n" );
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