document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114450>Question 114450</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rationalize the denominators\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+7+%29+-+sqrt%28+6+%29 ALIGN=MIDDLE  ALT=\"+sqrt%28+7+%29+-+sqrt%28+6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > / <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+7+%29+%2B+sqrt%28+6+%29 ALIGN=MIDDLE  ALT=\"+sqrt%28+7+%29+%2B+sqrt%28+6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Combine<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8sqrt%28+12+%29+-+3sqrt%28+27+%29+ ALIGN=MIDDLE  ALT=\"+8sqrt%28+12+%29+-+3sqrt%28+27+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<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 #83269 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=83269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+7+%29+-+sqrt%28+6+%29 ALIGN=MIDDLE  ALT=\"+sqrt%28+7+%29+-+sqrt%28+6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > / <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+7+%29+%2B+sqrt%28+6+%29 ALIGN=MIDDLE  ALT=\"+sqrt%28+7+%29+%2B+sqrt%28+6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To rationalize a denominator that is the sum or difference of two square roots, you need to recall the factorization of the difference of two squares, namely:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%28a-b%29=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%28a-b%29=a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you multiply the denominator of your fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%29-sqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%287%29-sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you will get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-6 ALIGN=MIDDLE  ALT=\"7-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > for your new denominator.  But in order to introduce that factor into the denominator, you have to multiply the entire fraction by 1 in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%287%29-sqrt%286%29%29%2F%28sqrt%287%29-sqrt%286%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%287%29-sqrt%286%29%29%2F%28sqrt%287%29-sqrt%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here is the entire expression:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28sqrt%28+7+%29+-+sqrt%28+6+%29%29%2F%28sqrt%28+7+%29+%2B+sqrt%28+6+%29%29%29%2A%28%28sqrt%287%29-sqrt%286%29%29%2F%28sqrt%287%29-sqrt%286%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Now, multiply the binomials and simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%287-2sqrt%287%29sqrt%286%29%2B6%29%2F%287-6%29 ALIGN=MIDDLE  ALT=\"+%287-2sqrt%287%29sqrt%286%29%2B6%29%2F%287-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-2sqrt%2842%29 ALIGN=MIDDLE  ALT=\"1-2sqrt%2842%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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