document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164947>Question 164947</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Perform the indicated operations and reduce to lowest terms<BR>\n" );
document.write( "2/x-3+3/3-x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121570 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am guessing that you have left out some parenthesis().  If in doubt put parenthesis around nearly everything.  I think the problem is supposed to be 2/(x-3)+3/(3-x)  which looks like this:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x-3%29%2B3%2F%283-x%29 ALIGN=MIDDLE  ALT=\"2%2F%28x-3%29%2B3%2F%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "However the problem that you wrote would have looked like this:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fx-3%2B3%2F3-x ALIGN=MIDDLE  ALT=\"2%2Fx-3%2B3%2F3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "With that said...<BR>\n" );
document.write( "in order to add two numbers they must have the same denominator.  If we look at the denominators:x-3 and 3-x we notice that one of them is the exact opposite of the other or the negative.  So factor out a -1 from 3-x and you get -1(-3+x) which can be written -1(x-3)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So now we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x-3%29%2B3%2F%28-1%28x-3%29%29 ALIGN=MIDDLE  ALT=\"2%2F%28x-3%29%2B3%2F%28-1%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply the top and bottom of: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28-1%28x-3%29%29 ALIGN=MIDDLE  ALT=\"3%2F%28-1%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by -1<BR>\n" );
document.write( "and you get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"-3%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the whole formula can be written <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x-3%29-3%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"2%2F%28x-3%29-3%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the denominators are the same now we can add the two expressions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-3%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%282-3%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"-1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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