document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=553022>Question 553022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> combine and simplify:\r<BR>\n" );
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document.write( "3x/(x+2) + x/(x-2) - 4x/(x^2-4)\r<BR>\n" );
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document.write( "the answer is 4x/(x+2), but I can't figure out how to get it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360640 by </B><A HREF=/tutors/aboutme.mpl?userid=TutorDelphia><B>TutorDelphia(193)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TutorDelphia><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=TutorDelphia><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=360640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Like all fraction addition, the first thing we have to do is get the denominators the same. \r<BR>\n" );
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document.write( "Your teacher gave you a problem that works out relatively easily if you know the trick. The trick is the (x+2)*(x-2)=x^2-4. This is called the difference of two squares and you can find more info on it here: http://www.themathpage.com/alg/difference-two-squares.htm\r<BR>\n" );
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document.write( "So my common denominator will be x^2-4\r<BR>\n" );
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document.write( "To get the first fraction to equal that on the denominator I have to multiply by (x-2), for the second fraction, I have to multiply by x+2 and the third is already set\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2F%28x%2B2%29%29%2A%28%28x-2%29%2F%28x-2%29%29%2B%28x%2F%28x-2%29%29%2A%28%28x%2B2%29%2F%28x%2B2%29%29-%284x%2F%28x%5E2-4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can distribute the bottoms and get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%2A%28x-2%29%2F%28x%5E2-4%29%2B%28x%2A%28x%2B2%29%29%2F%28x%5E2-4%29-4x%2F%28x%5E2-4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the denominator is all the same, I can now add or subtract the tops:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2A%28x-2%29%2Bx%2A%28x%2B2%29-4x%29+%2F%28x%5E2-4%29 ALIGN=MIDDLE  ALT=\"%283x%2A%28x-2%29%2Bx%2A%28x%2B2%29-4x%29+%2F%28x%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distributing the tops gets me<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2-6x%2Bx%5E2%2B2x-4x%29%2F%28x%5E2-4%29 ALIGN=MIDDLE  ALT=\"%283x%5E2-6x%2Bx%5E2%2B2x-4x%29%2F%28x%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combining like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2-8x%29%2F%28x%5E2-4%29 ALIGN=MIDDLE  ALT=\"%284x%5E2-8x%29%2F%28x%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's factor out a 4x from the top\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%28x-2%29%29%2F%28x%5E2-4%29 ALIGN=MIDDLE  ALT=\"%284x%28x-2%29%29%2F%28x%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4=%28x%2B2%29%28x-2%29 ALIGN=MIDDLE  ALT=\"x%5E2-4=%28x%2B2%29%28x-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=4x%28x-2%29%2F%28x%2B2%29%28x-2%29 ALIGN=MIDDLE  ALT=\"4x%28x-2%29%2F%28x%2B2%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the x-2 cancels out and we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"4x%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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