document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=225816>Question 225816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sqrt%28a%29%2Bsqrt%28a%2B1%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28sqrt%28a%29%2Bsqrt%28a%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%2B1%29-sqrt%28a%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%2B1%29-sqrt%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hence, deduce the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%28sqrt%281%29%2Bsqrt%282%29%29 ALIGN=MIDDLE  ALT=\"+1%2F%28sqrt%281%29%2Bsqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sqrt%282%29%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28sqrt%282%29%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sqrt%283%29%2Bsqrt%284%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28sqrt%283%29%2Bsqrt%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + ... + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sqrt%288%29%2Bsqrt%289%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28sqrt%288%29%2Bsqrt%289%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Please help and thanks for helping ! :D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #168355 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=168355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "First, see my lesson on Rationalizing The Denominator: http://www.algebra.com/algebra/homework/Radicals/rationalizingdenominators1.lesson\r<BR>\n" );
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document.write( "The multiplier that is necessary for this particular problem is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{1}{\sqrt{a}+\sqrt{a+1}}\right)\left(\frac{\sqrt{a}-\sqrt{a+1}}{\sqrt{a}-\sqrt{a+1}}\right)\ =\ \frac{\sqrt{a}-\sqrt{a+1}}{a-(a+1)}\ =\ \frac{\sqrt{a}-\sqrt{a+1}}{-1}\ =\ -\left(\sqrt{a}-\sqrt{a+1}\right)\ =\ \sqrt{a+1}-\sqrt{a}\">\r<BR>\n" );
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document.write( "Once you convert all the terms using the rule just developed, and collect like terms, you will notice that all of the terms will disappear except for -1 and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{9} = 3\">, hence the sum is 2.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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