document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=986716>Question 986716</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the limit, if it exisit lim goes to 3 of 1/x-1/3/x-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #607584 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=607584\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's simplify the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx+-+1%2F3%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%281%2Fx+-+1%2F3%29%2F%28x-3%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=%28red%283x%29%2A%281%2Fx+-+1%2F3%29%29%2F%28red%283x%29%2A%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28red%283x%29%2A%281%2Fx+-+1%2F3%29%29%2F%28red%283x%29%2A%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply top and bottom by the inner LCD 3x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28red%283x%29%2A%281%2Fx%29+-+red%283x%29%2A%281%2F3%29%29%2F%28red%283x%29%2A%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28red%283x%29%2A%281%2Fx%29+-+red%283x%29%2A%281%2F3%29%29%2F%28red%283x%29%2A%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute through the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-x%29%2F%283x%2A%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%283-x%29%2F%283x%2A%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply. Notice how the upper fractions go away\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-3%2Bx%29%29%2F%283x%2A%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28-%28-3%2Bx%29%29%2F%283x%2A%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out -1 from the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28x-3%29%29%2F%283x%2A%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28-%28x-3%29%29%2F%283x%2A%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2Across%28%28x-3%29%29%29%2F%283x%2Across%28%28x-3%29%29%29 ALIGN=MIDDLE  ALT=\"%28-1%2Across%28%28x-3%29%29%29%2F%283x%2Across%28%28x-3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "Now plug in x = 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%283%2A3%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%283%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace every 'x' with 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F9 ALIGN=MIDDLE  ALT=\"-1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \lim_{x \to 3} \left( \frac{\frac{1}{x}-\frac{1}{3}}{x-3} \right) = -\frac{1}{9}\">\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "If you need more help, or if you have any questions about the problem, feel free to email me at <font color=\"blue\"><code>jim_thompson5910@hotmail.com</code></font> </SPAN>\n" );
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