document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74127>Question 74127</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x+5/x-5+3/x+5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53190 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=53190\">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=x%2B5%2Fx-5%2B3%2Fx%2B5 ALIGN=MIDDLE  ALT=\"x%2B5%2Fx-5%2B3%2Fx%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Because you didn't use parentheses, the rules of math say that your problem should be interpreted<BR>\n" );
document.write( "as above.<BR>\n" );
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document.write( "In simplifying that problem, note that the +5 and the -5 cancel each other.  Then the two terms<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fx ALIGN=MIDDLE  ALT=\"5%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fx ALIGN=MIDDLE  ALT=\"3%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be added to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fx ALIGN=MIDDLE  ALT=\"8%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > and these to operations reduce your problem<BR>\n" );
document.write( "to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+%288%2Fx%29 ALIGN=MIDDLE  ALT=\"x+%2B+%288%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This can be further simplified by getting the two terms to have a common denominator of<BR>\n" );
document.write( "x.  Do this by multiplying the x by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx ALIGN=MIDDLE  ALT=\"x%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equivalent to multiplying the x by 1<BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx ALIGN=MIDDLE  ALT=\"x%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to 1<BR>\n" );
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document.write( "The expression is then:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Fx%29+%2B+%288%2Fx%29+=+%28x%5E2+%2B+8%29%2Fx%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Fx%29+%2B+%288%2Fx%29+=+%28x%5E2+%2B+8%29%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "and that's the simplification of the expression the way you wrote it.  If you had used<BR>\n" );
document.write( "parentheses to lump things together, I think you meant to write:<BR>\n" );
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document.write( "(x+5)/(x-5) - (3/(x+5))<BR>\n" );
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document.write( "And that would translate to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B5%29%2F%28x-5%29%29+-+%283%2F%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%2F%28x-5%29%29+-+%283%2F%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And as you can see, that's a whole different problem.  Parentheses are very important if you<BR>\n" );
document.write( "are trying to communicate what you really mean.<BR>\n" );
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document.write( "To solve this problem, we again need to get a common denominator.  That denominator is <BR>\n" );
document.write( "(x-5)*(x+5).<BR>\n" );
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document.write( "To get the first term over the common denominator multiply it by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This multiplication is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B5%29%2F%28x-5%29%29%2A%28%28x%2B5%29%2F%28x%2B5%29%29+=+%28x%2B5%29%5E2%2F%28%28x-5%29%2A%28x%2B5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And if you square the numerator it becomes :<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+10x+%2B+25%29%2F%28%28x-5%29%2A%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+10x+%2B+25%29%2F%28%28x-5%29%2A%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That takes care of the first part of the problem.  The second part consists of placing the second<BR>\n" );
document.write( "term over the common denominator also.  Recall that the second term was:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+%283%2F%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"-+%283%2F%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Put it over the common denominator by multiplying it by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%2F%28x-5%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%2F%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This 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=-%283%2F%28x%2B5%29%29%2A%28%28x-5%29%2F%28x-5%29%29=+-3%2A%28x-5%29%2F%28%28x-5%29%2A%28x%2B5%29%29+=+%28-3x+%2B+15%29%2F%28%28x-5%29%2A%28x%2B5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we can get the total answer because the two terms are over a common denominator. <BR>\n" );
document.write( "Because of that we can add the numerators of the two terms and place the sum over the <BR>\n" );
document.write( "common denominator.  The first term plus the second term is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+10x+%2B+25%29%2F%28%28x-5%29%2A%28x%2B5%29%29%2B%28-3x+%2B+15%29%2F%28%28x-5%29%2A%28x%2B5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The numerator of the combination becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10x+%2B+25+-+3x+%2B+15 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10x+%2B+25+-+3x+%2B+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And this simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+7x+%2B+40 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+7x+%2B+40\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Putting this over the common denominator<BR>\n" );
document.write( "makes the answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+7x+%2B+40%29%2F%28%28x-5%29%2A%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+7x+%2B+40%29%2F%28%28x-5%29%2A%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "And if you multiply out the common denominator, the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+7x+%2B+40%29%2F%28x%5E2+-+25%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+7x+%2B+40%29%2F%28x%5E2+-+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "I hope this impresses you with the difference in the two interpretations of the problem you<BR>\n" );
document.write( "presented.  The use of parentheses make these two answers completely different and shows<BR>\n" );
document.write( "why it's so important to group terms to say what you really mean.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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