document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1009964>Question 1009964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1-Find an equation of the tangent line to the graph of f(x)=(x^3+1)/(x^2+x+1)<BR>\n" );
document.write( "at the point whose x-coordinate is 1.\r<BR>\n" );
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document.write( "2-Find the equation of the tangent line to the curve   at the point (4,1).<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 #625445 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=625445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The slope in general would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdx=m=%28%28x%5E2%2Bx%2B1%29%283x%5E2%29-%28x%5E3%2B1%29%282x%2B1%29%29%2F%28x%5E2%2Bx%2B1%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the steps to simplify not shown here,...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28x%5E4%2B2x%5E3%2B3x%5E2-2x-1%29%2F%28x%5E2%2Bx%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"m=%28x%5E4%2B2x%5E3%2B3x%5E2-2x-1%29%2F%28x%5E2%2Bx%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "For the point whose x coordinate is 1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=y=%281%5E3%2B1%29%2F%281%5E2%2B1%2B1%29 ALIGN=MIDDLE  ALT=\"f%281%29=y=%281%5E3%2B1%29%2F%281%5E2%2B1%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=y=2%2F4=1%2F2 ALIGN=MIDDLE  ALT=\"f%281%29=y=2%2F4=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the point being  (1, 1/2).\r<BR>\n" );
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document.write( "The slope for x=1, according to the formula found for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=df%2Fdx ALIGN=MIDDLE  ALT=\"m=df%2Fdx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%5E3%2B2%2A1%5E3%2B3%2A1%5E2-2%2A1-1%29%2F%282%5E2%29 ALIGN=MIDDLE  ALT=\"%281%5E3%2B2%2A1%5E3%2B3%2A1%5E2-2%2A1-1%29%2F%282%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "Then if using point-slope linear equation form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y-1%2F2=%283%2F4%29%28x-1%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y-1%2F2=%283%2F4%29%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or put into slope-intercept form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F4%29x-3%2F4%2B1%2F2 ALIGN=MIDDLE  ALT=\"y=%283%2F4%29x-3%2F4%2B1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%283%2F4%29x-3%2F4%2B2%2F4 ALIGN=MIDDLE  ALT=\"y=%283%2F4%29x-3%2F4%2B2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%283%2F4%29x-1%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%283%2F4%29x-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The other question can then be handled much the same, just re-using the formula for the slope and the given point.\r<BR>\n" );
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document.write( "---<BR>\n" );
document.write( "The mnemonic for formula of derivative of a rational function goes as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ho%2Adhi-hi%2Adho%29%2F%28ho%2Aho%29 ALIGN=MIDDLE  ALT=\"%28ho%2Adhi-hi%2Adho%29%2F%28ho%2Aho%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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