document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=97111>Question 97111</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321279069/algebrahomeworkh>precalculus graphs and models</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Alrighty, here is the question, \r<BR>\n" );
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document.write( "          6<BR>\n" );
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document.write( "        3+ sqrt 5    , I know that you have to use the conjugates when the same # with the different sign in the middle, so it should then look like this <BR>\n" );
document.write( "         6     3-sqrt5      18 +6sqrt 5<BR>\n" );
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document.write( "     3+sqrt 5  3-sqrt 5\r<BR>\n" );
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document.write( "then I think you foil the denominator, and get (3+sqrt5)(3-sqrt5), and this = to 9+3-sqrt5+3+sqrt5, and sqrt -5 and sqrt 5=-25, =-5and the middle cancels out and leaves you with 9-5=4 but the answer in the back of book is 9-3sqrt5<BR>\n" );
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document.write( "how did they get that? thank you for your time.  Stacy<BR>\n" );
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 #70677 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=70677\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming you want to rationalize the denominator right?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%283%2Bsqrt%285%29%29 ALIGN=MIDDLE  ALT=\"6%2F%283%2Bsqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F%283%2Bsqrt%285%29%29%29%28%283-sqrt%285%29%29%2F%283-sqrt%285%29%29%29 ALIGN=MIDDLE  ALT=\"%286%2F%283%2Bsqrt%285%29%29%29%28%283-sqrt%285%29%29%2F%283-sqrt%285%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-sqrt%285%29%29%2F%283-sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"%283-sqrt%285%29%29%2F%283-sqrt%285%29%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=6%283-sqrt%285%29%29%2F%283%2Bsqrt%285%29%29%283-sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"6%283-sqrt%285%29%29%2F%283%2Bsqrt%285%29%29%283-sqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%283-sqrt%285%29%29%2F%283%2A3-3%2Asqrt%285%29%2B3sqrt%285%29-sqrt%285%29%2Asqrt%285%29%29 ALIGN=MIDDLE  ALT=\"6%283-sqrt%285%29%29%2F%283%2A3-3%2Asqrt%285%29%2B3sqrt%285%29-sqrt%285%29%2Asqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%283-sqrt%285%29%29%2F%283%2A3%2Bcross%28-3%2Asqrt%285%29%2B3sqrt%285%29%29-sqrt%285%29%2Asqrt%285%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Combine and cancel out like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%283-sqrt%285%29%29%2F%289-5%29 ALIGN=MIDDLE  ALT=\"6%283-sqrt%285%29%29%2F%289-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%283-sqrt%285%29%29%2F4 ALIGN=MIDDLE  ALT=\"6%283-sqrt%285%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%283-sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"3%283-sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F4 ALIGN=MIDDLE  ALT=\"6%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is probably where you got lost. You should have reduced before you distributed.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-3%2Asqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"%289-3%2Asqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Plug in the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%283%2Bsqrt%285%29%29 ALIGN=MIDDLE  ALT=\"6%2F%283%2Bsqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into your calculator to approximately get 1.14589803375031\r<BR>\n" );
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document.write( "Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-3%2Asqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"%289-3%2Asqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into your calculator to approximately get 1.14589803375031\r<BR>\n" );
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document.write( "Since they are equivalent, (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%283%2Bsqrt%285%29%29=%289-3%2Asqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"6%2F%283%2Bsqrt%285%29%29=%289-3%2Asqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) this verifies our answer </SPAN>\n" );
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