document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407910>Question 407910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify by rationalising the denominator\r<BR>\n" );
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document.write( "[(sqrt10)+(2sqrt5)]/[(sqrt10)+(sqrt5)] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287441 by </B><A HREF=/tutors/aboutme.mpl?userid=graphmatics><B>graphmatics(170)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=graphmatics><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=graphmatics><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=287441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are given the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2F%28sqrt%2810%29%2Bsqrt%285%29%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2F%28sqrt%2810%29%2Bsqrt%285%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In general when there are radicals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28a%29%2Bsqrt%28c%29%29%2F%28sqrt%28a%29%2Bsqrt%28b%29%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%28a%29%2Bsqrt%28c%29%29%2F%28sqrt%28a%29%2Bsqrt%28b%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the denominator of a fraction<BR>\n" );
document.write( "we multiply the fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28a%29-sqrt%28b%29%29%2F%28sqrt%28a%29-sqrt%28b%29%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%28a%29-sqrt%28b%29%29%2F%28sqrt%28a%29-sqrt%28b%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(example: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28sqrt%28a%29%2Bsqrt%28b%29%29+ ALIGN=MIDDLE  ALT=\"1%2F%28sqrt%28a%29%2Bsqrt%28b%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F%28sqrt%28a%29%2Bsqrt%28b%29%29%29%2A%28%28sqrt%28a%29-sqrt%28b%29%29%2F%28sqrt%28a%29-sqrt%28b%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So for the given expression we have that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2F%28sqrt%2810%29%2Bsqrt%285%29%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2F%28sqrt%2810%29%2Bsqrt%285%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2F%28sqrt%2810%29%2Bsqrt%285%29%29%29%2A%28%28sqrt%2810%29-sqrt%285%29%29%2F%28sqrt%2810%29-sqrt%285%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2A%28sqrt%2810%29-sqrt%285%29%29%29%2F%28sqrt%2810%29%2Asqrt%2810%29-sqrt%2810%29%2Asqrt%285%29%2Bsqrt%285%29%2Asqrt%2810%29-sqrt%285%29%2Asqrt%285%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2A%28sqrt%2810%29-sqrt%285%29%29%29%2F%2810-5%29%29+ ALIGN=MIDDLE  ALT=\"%28%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2A%28sqrt%2810%29-sqrt%285%29%29%29%2F%2810-5%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2A%28sqrt%2810%29-sqrt%285%29%29%29%2F%285%29%29+ ALIGN=MIDDLE  ALT=\"%28%28sqrt%2810%29%2B2%2Asqrt%285%29%29%2A%28sqrt%2810%29-sqrt%285%29%29%29%2F%285%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We will simplify the numerator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2810%29%2Asqrt%2810%29-sqrt%2810%29sqrt%285%29%2B2%2Asqrt%285%29%2Asqrt%2810%29-2%2Asqrt%285%29%2Asqrt%285%29%29%2F%285%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2810%29%2Asqrt%285%29%29%2F%285%29%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%2810%29%2Asqrt%285%29%29%2F%285%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%2A5%29%2Asqrt%285%29%29%2F%285%29%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%282%2A5%29%2Asqrt%285%29%29%2F%285%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29%2A5%29%2F%285%29%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%282%29%2A5%29%2F%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=sqrt%282%29+ ALIGN=MIDDLE  ALT=\"sqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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