document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72429>Question 72429</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Adding and Subtracting Radical Expressions:\r<BR>\n" );
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document.write( "Perform the operation and Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%29%2F%28x%2By%29+ ALIGN=MIDDLE  ALT=\"+%285%29%2F%28x%2By%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%29%2F%28x%5E2-y%5E2%29+ ALIGN=MIDDLE  ALT=\"+%285%29%2F%28x%5E2-y%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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 #51756 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=51756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To simplify this expression, you can first note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+-+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the difference<BR>\n" );
document.write( "of two squares.  Therefore, it factors into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+y%29%2A+%28x+%2B+y%29 ALIGN=MIDDLE  ALT=\"%28x+-+y%29%2A+%28x+%2B+y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substitute these and<BR>\n" );
document.write( "the problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%29%2F%28x%2By%29+%2B+%285%29%2F%28%28x-y%29%2A%28x%2By%29%29 ALIGN=MIDDLE  ALT=\"+%285%29%2F%28x%2By%29+%2B+%285%29%2F%28%28x-y%29%2A%28x%2By%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the first fraction lacks a (x-y) term in the denominator.  If it had one, then<BR>\n" );
document.write( "this first fraction could be combined with the second fraction because they both would have<BR>\n" );
document.write( "the same denominator.<BR>\n" );
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document.write( "Let's multiply the first fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29%2F%28x-y%29 ALIGN=MIDDLE  ALT=\"%28x-y%29%2F%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Because the numerator is identical to<BR>\n" );
document.write( "the denominator in this multiplier, it is equivalent to multiplying by 1.  The multiplication<BR>\n" );
document.write( "results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%285%29%2F%28x%2By%29%29%2A%28%28x-y%29%2F%28x-y%29%29+%2B+%285%29%2F%28%28x-y%29%2A%28x%2By%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since the two fractions now have a common denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29%2A%28x%2By%29 ALIGN=MIDDLE  ALT=\"%28x-y%29%2A%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > their numerators<BR>\n" );
document.write( "may be put over this common denominator to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A%28x-y%29%2B5%29%2F%28%28x-y%29%2A%28x%2By%29%29 ALIGN=MIDDLE  ALT=\"%285%2A%28x-y%29%2B5%29%2F%28%28x-y%29%2A%28x%2By%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then, doing the multiplication in the numerator results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2Ax+-+5%2Ay+%2B+5%29%2F%28%28x-y%29%2A%28x%2By%29%29 ALIGN=MIDDLE  ALT=\"%285%2Ax+-+5%2Ay+%2B+5%29%2F%28%28x-y%29%2A%28x%2By%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And factoring the common 5 in the numerator:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x+-+y+%2B1%29%2F%28%28x-y%29%2A%28x%2By%29%29 ALIGN=MIDDLE  ALT=\"5%2A%28x+-+y+%2B1%29%2F%28%28x-y%29%2A%28x%2By%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this gives you some additional insight into working with fractional expressions. </SPAN>\n" );
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