document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149635>Question 149635</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Add and Simplify:<BR>\n" );
document.write( "1/x-2 - 4/x^2-4 + 3/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 #109766 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=109766\">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=1%2F%28x-2%29+-+4%2F%28x%5E2-4%29+%2B+3%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-2%29+-+4%2F%28x%5E2-4%29+%2B+3%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-2%29+-+4%2F%28%28x-2%29%28x%2B2%29%29+%2B+3%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-2%29+-+4%2F%28%28x-2%29%28x%2B2%29%29+%2B+3%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4 ALIGN=MIDDLE  ALT=\"x%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B2%29%2F%28x%2B2%29%29%281%2F%28x-2%29%29+-+4%2F%28%28x-2%29%28x%2B2%29%29+%2B+%28%28x-2%29%2F%28x-2%29%29%283%2F%28x%2B2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Multiply the third fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Doing this will make each denominator the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2F%28x-2%29%28x%2B2%29+-+4%2F%28%28x-2%29%28x%2B2%29%29+%2B+%283%28x-2%29%29%2F%28x-2%29%28x%2B2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2F%28x-2%29%28x%2B2%29+-+4%2F%28%28x-2%29%28x%2B2%29%29+%2B+%283x-6%29%2F%28x-2%29%28x%2B2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2-4%2B3x-6%29%2F%28%28x-2%29%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B2-4%2B3x-6%29%2F%28%28x-2%29%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since the denominators are equal, we can combine the numerators of the common denominator. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x-8%29%2F%28%28x-2%29%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%284x-8%29%2F%28%28x-2%29%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%28x-2%29%29%2F%28%28x-2%29%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%284%28x-2%29%29%2F%28%28x-2%29%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF 4 from the numerator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284highlight%28%28x-2%29%29%29%2F%28highlight%28%28x-2%29%29%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%284highlight%28%28x-2%29%29%29%2F%28highlight%28%28x-2%29%29%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284cross%28%28x-2%29%29%29%2F%28cross%28%28x-2%29%29%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%284cross%28%28x-2%29%29%29%2F%28cross%28%28x-2%29%29%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%284%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-2%29+-+4%2F%28x%5E2-4%29+%2B+3%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-2%29+-+4%2F%28x%5E2-4%29+%2B+3%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%284%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-2%29-4%2F%28x%5E2-4%29%2B3%2F%28x%2B2%29=%284%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-2%29-4%2F%28x%5E2-4%29%2B3%2F%28x%2B2%29=%284%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-2 ALIGN=MIDDLE  ALT=\"x%3C%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E2 ALIGN=MIDDLE  ALT=\"x%3C%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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