document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=344844>Question 344844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> finding the difference quotient\r<BR>\n" );
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document.write( "f(x+h)-f(x)/h\r<BR>\n" );
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document.write( " g(x)=3sqrt of x<BR>\n" );
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document.write( "I can set it up but i can't get the right answer\r<BR>\n" );
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document.write( "3 sqrt x+h - 3sqrt of x/ h\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #246735 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=246735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are exactly correct so far:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283sqrt%28x%2Bh%29+-+3sqrt%28x%29%29%2F+h ALIGN=MIDDLE  ALT=\"%283sqrt%28x%2Bh%29+-+3sqrt%28x%29%29%2F+h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As h approaches 0, this is still of the 0/0 form so we need to do more. With experience you will learn that the next step is to multiply the numerator and denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283sqrt%28+x%2Bh%29+%2B+3sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"%283sqrt%28+x%2Bh%29+%2B+3sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. (You will see why after you see how this simplifies things.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283sqrt%28+x%2Bh%29+-+3sqrt%28x%29%29%2F+h%29%28%283sqrt%28+x%2Bh%29+%2B+3sqrt%28x%29%29%2F%283sqrt%28+x%2Bh%29+%2B+3sqrt%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the numerator we can take advantage of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern. (We'll leave the denominator factored for reasons you will see shortly.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283sqrt%28+x%2Bh%29%29%5E2+-+%283sqrt%28x%29%29%5E2%29%2F+%28%28h%29%283sqrt%28+x%2Bh%29+%2B+3sqrt%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying the numerator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%28x%2Bh%29+-+%289x%29%29%2F+%28%28h%29%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29%29 ALIGN=MIDDLE  ALT=\"%289%28x%2Bh%29+-+%289x%29%29%2F+%28%28h%29%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x+%2B+9h+-+9x%29%2F+%28%28h%29%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29%29 ALIGN=MIDDLE  ALT=\"%289x+%2B+9h+-+9x%29%2F+%28%28h%29%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9h%2F%28%28h%29%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29%29 ALIGN=MIDDLE  ALT=\"9h%2F%28%28h%29%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At this point we will reduce the fraction. (And we can see why we didn't bother multiplying out the denominator.) The h's cancel:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9cross%28h%29%2F%28cross%28h%29%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29%29 ALIGN=MIDDLE  ALT=\"9cross%28h%29%2F%28cross%28h%29%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"9%2F%283sqrt%28x%2Bh%29+%2B+3sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can factor out a 3 in the denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%283%28sqrt%28x%2Bh%29+%2B+sqrt%28x%29%29%29 ALIGN=MIDDLE  ALT=\"9%2F%283%28sqrt%28x%2Bh%29+%2B+sqrt%28x%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And cancel a factor of 3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28sqrt%28x%2Bh%29+%2B+sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"3%2F%28sqrt%28x%2Bh%29+%2B+sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the difference quotient. (As h approaches 0, this fraction is not of the 0/0 form.) </SPAN>\n" );
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