document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1095036>Question 1095036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I determine the difference quotient (simplify when possible)?\r<BR>\n" );
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document.write( "g(x) = x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #709663 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=709663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">First compute g(x+h):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+x%5E2 ALIGN=MIDDLE  ALT=\"g%28x%29+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%2Bh%29+=+%28x%2Bh%29%5E2 ALIGN=MIDDLE  ALT=\"g%28x%2Bh%29+=+%28x%2Bh%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace every x with x+h\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%2Bh%29+=+%28x%2Bh%29%28x%2Bh%29 ALIGN=MIDDLE  ALT=\"g%28x%2Bh%29+=+%28x%2Bh%29%28x%2Bh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%2Bh%29+=+x%28x%2Bh%29%2Bh%28x%2Bh%29 ALIGN=MIDDLE  ALT=\"g%28x%2Bh%29+=+x%28x%2Bh%29%2Bh%28x%2Bh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%2Bh%29+=+x%5E2%2Bxh%2Bxh%2Bh%5E2 ALIGN=MIDDLE  ALT=\"g%28x%2Bh%29+=+x%5E2%2Bxh%2Bxh%2Bh%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%2Bh%29+=+x%5E2%2B2xh%2Bh%5E2 ALIGN=MIDDLE  ALT=\"g%28x%2Bh%29+=+x%5E2%2B2xh%2Bh%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "Now find the Difference Quotient:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%28x%5E2%2B2xh%2Bh%5E2+-+x%5E2%29%2Fh ALIGN=MIDDLE  ALT=\"%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%28x%5E2%2B2xh%2Bh%5E2+-+x%5E2%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%282xh%2Bh%5E2%29%2Fh ALIGN=MIDDLE  ALT=\"%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%282xh%2Bh%5E2%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Note how the x^2 terms subtract and cancel \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%28h%282x%2Bh%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%28h%282x%2Bh%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF h\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%28cross%28h%29%282x%2Bh%29%29%2F%28cross%28h%29%29 ALIGN=MIDDLE  ALT=\"%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+%28cross%28h%29%282x%2Bh%29%29%2F%28cross%28h%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide the h terms and cancel\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+2x%2Bh ALIGN=MIDDLE  ALT=\"%28g%28x%2Bh%29+-+g%28x%29%29%2Fh+=+2x%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So when everything is fully simplified, the final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Bh ALIGN=MIDDLE  ALT=\"2x%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" ></font> </SPAN>\n" );
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