document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066423>Question 1066423</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the difference quotient f(x+h)-f(x)/h, where h cannot be equal to 0 , for the function below. <BR>\n" );
document.write( "f(x)=1/x+9\r<BR>\n" );
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document.write( "Simplify your answer as much as possible.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681614 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=681614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [f(x+h)-f(x)]/h=<BR>\n" );
document.write( "[(1/(x+h+9))-(1/(x+9))]/h=<BR>\n" );
document.write( "common denominator is (x+h+9)(x+9)<BR>\n" );
document.write( "numerator is x+9-(x+h+9)=-h<BR>\n" );
document.write( "so the quotient is -h/h(x+h+9)(x+9), bringing the h in below.<BR>\n" );
document.write( "When we use f(x+h)-f(x)/h, and let h approach 0, we have -1/(x+9)^2, which is the derivative of 1/(x+9). </SPAN>\n" );
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