document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=17582>Question 17582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can some one please show me how to rationalize the denominator in this problem?<BR>\n" );
document.write( "1 / 2 + radical x<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 #8489 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=8489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming that your problem is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282%2B+sqrt%28x%29%29+ ALIGN=MIDDLE  ALT=\"1%2F%282%2B+sqrt%28x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since this is a binomial denominator (two terms!), you must multiply numerator and denominator by the conjugate of the denominator--that is, the same as the denominator, but with the oppposite sign in the middle.\r<BR>\n" );
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document.write( "It looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282%2B+sqrt%28x%29%29+ ALIGN=MIDDLE  ALT=\"1%2F%282%2B+sqrt%28x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-sqrt%28x%29%29%2F%282-sqrt%28x%29%29+ ALIGN=MIDDLE  ALT=\"%282-sqrt%28x%29%29%2F%282-sqrt%28x%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When you expand the denominator, the middle terms subtract out (as they ALWAYS do!), and the denominator is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+-+x ALIGN=MIDDLE  ALT=\"4+-+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This has no radicals, so it is said to be rationalized.\r<BR>\n" );
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document.write( "Final answer:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282-sqrt%28x%29%29%2F%284-x%29+ ALIGN=MIDDLE  ALT=\"+%282-sqrt%28x%29%29%2F%284-x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "R^2 at SCC<BR>\n" );
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