document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628430>Question 628430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> which choice is equivalent to the fraction below when x>or equal to 2?\r<BR>\n" );
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document.write( "4/&#8730; (x-2)-&#8730; x\r<BR>\n" );
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document.write( "A) -2(&#8730; x+&#8730; x-2)<BR>\n" );
document.write( "B) 2(&#8730; x+&#8730; x-2)<BR>\n" );
document.write( "C) -2(&#8730; x-&#8730; x-2)<BR>\n" );
document.write( "D) 2(&#8730; x-&#8730; x-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395675 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=395675\">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=4%2F%28sqrt%28x-2%29-sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"4%2F%28sqrt%28x-2%29-sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that none of the answers are fractions. This means that the fraction above must have had its denominator rationalized and that the resulting fraction reduced to the point that there is no longer any fraction. So what we need to do is rationalize the denominator.<br><BR>\n" );
document.write( "Rationalizing a two-term denominator like yours takes advantage of the <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;\" > pattern. This pattern shows us how to take a tw0-term expression (an a+b or an a-b), multiply it by something and get an expression of perfect squares. With your denominator having a \"-\" between the terms, it will play the role of a-b. So to get the perfect squares we are looking for, we need to multiply by a+b:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F%28sqrt%28x-2%29-sqrt%28x%29%29%29%28%28sqrt%28x-2%29%2Bsqrt%28x%29%29%2F%28sqrt%28x-2%29%2Bsqrt%28x%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On top we use the Distributive Property to multiply. On the bottom the pattern tells us how it will work out:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Asqrt%28x-2%29%2B4%2Asqrt%28x%29%29%2F%28%28sqrt%28x-2%29%29%5E2-%28sqrt%28x%29%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Asqrt%28x-2%29%2B4%2Asqrt%28x%29%29%2F%28%28x-2%29-%28x%29%29 ALIGN=MIDDLE  ALT=\"%284%2Asqrt%28x-2%29%2B4%2Asqrt%28x%29%29%2F%28%28x-2%29-%28x%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=%284%2Asqrt%28x-2%29%2B4%2Asqrt%28x%29%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"%284%2Asqrt%28x-2%29%2B4%2Asqrt%28x%29%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%282%2Asqrt%28x-2%29%2B4%2Asqrt%28x%29%29%29%2F%28%28-1%29%2A2%29 ALIGN=MIDDLE  ALT=\"%282%282%2Asqrt%28x-2%29%2B4%2Asqrt%28x%29%29%29%2F%28%28-1%29%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%282%29%282%2Asqrt%28x-2%29%2B2%2Asqrt%28x%29%29%29%2F%28%28-1%29%2Across%282%29%29 ALIGN=MIDDLE  ALT=\"%28cross%282%29%282%2Asqrt%28x-2%29%2B2%2Asqrt%28x%29%29%29%2F%28%28-1%29%2Across%282%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=%282%2Asqrt%28x-2%29%2B2%2Asqrt%28x%29%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%28x-2%29%2B2%2Asqrt%28x%29%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Asqrt%28x-2%29%2B%28-2%2Asqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"-2%2Asqrt%28x-2%29%2B%28-2%2Asqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the simplified expression. The answers given to you are factored. Factoring out -2 we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28sqrt%28x-2%29%2Bsqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"-2%28sqrt%28x-2%29%2Bsqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is equal to answer \"A\". </SPAN>\n" );
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