document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93035>Question 93035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> &#8730;3  -  &#8730;1/3\r<BR>\n" );
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document.write( "answer is 2&#8730;3<BR>\n" );
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document.write( "           3\r<BR>\n" );
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document.write( "I need to know how to get the answer.<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 #67765 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=67765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's one way of doing the problem:<BR>\n" );
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document.write( "Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29+-+sqrt%281%2F3%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29+-+sqrt%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Change the second term into the square root of the numerator over the square root of the <BR>\n" );
document.write( "denominator to make the given expression become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29+-+sqrt%281%29%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29+-+sqrt%281%29%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Put the first term over a common denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by multiplying the first term<BR>\n" );
document.write( "by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since the denominator and numerator of this multiplier are equal, <BR>\n" );
document.write( "this is equivalent to multiplying the first term by 1.  This multiplication makes the <BR>\n" );
document.write( "expression become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2Asqrt%283%29%2Fsqrt%283%29%29-+%28sqrt%281%29%2Fsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2Asqrt%283%29%2Fsqrt%283%29%29-+%28sqrt%281%29%2Fsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the numerator of the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Multiplying <BR>\n" );
document.write( "out the two square roots just results in an answer of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. And the numerator of the<BR>\n" );
document.write( "second term is the square root of 1. But the square root of 1 is just 1.  Making these two<BR>\n" );
document.write( "changes to the expression results in it becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fsqrt%283%29+-+1%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"3%2Fsqrt%283%29+-+1%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since both terms have a common denominator the two numerators can be combined over that <BR>\n" );
document.write( "common denominator and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283+-+1%29%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"+%283+-+1%29%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the subtraction in the numerator and the expression further simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"+2%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, by convention we do not leave a square root in the denominator. To get rid of it,<BR>\n" );
document.write( "just multiply the expression by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it transforms the expression:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Fsqrt%283%29%29+%2A+%28sqrt%283%29%2Fsqrt%283%29%29+=+2sqrt%283%29%2F%28sqrt%283%29%2Asqrt%283%29%29+=+2sqrt%283%29%2F3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And that's the answer you were looking for.<BR>\n" );
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document.write( "Hope this helps clarify the problem for you.<BR>\n" );
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