document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145505>Question 145505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 16           2(x-4)<BR>\n" );
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document.write( "x2-16        x+4\r<BR>\n" );
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document.write( "Adding Rational Expressions  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106153 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=106153\">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=%2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%29%2F%28x%2B4%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=%2816%29%2F%28%28x%2B4%29%28x-4%29%29%2B%282%28x-4%29%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%2816%29%2F%28%28x%2B4%29%28x-4%29%29%2B%282%28x-4%29%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-16 ALIGN=MIDDLE  ALT=\"x%5E2-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-4%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=%2816%29%2F%28%28x%2B4%29%28x-4%29%29%2B%28%28x-4%29%2F%28x-4%29%29%28%282%28x-4%29%29%2F%28x%2B4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x-4%29%2F%28x-4%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=%2816%29%2F%28%28x%2B4%29%28x-4%29%29%2B%282%28x-4%29%28x-4%29%29%2F%28%28x%2B4%29%28x-4%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=%2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%28x-4%29%29%2F%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"%2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%28x-4%29%29%2F%28x%5E2-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-16 ALIGN=MIDDLE  ALT=\"x%5E2-16\"   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=%2816%29%2F%28x%5E2-16%29%2B%282%28x%5E2-8x%2B16%29%29%2F%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"%2816%29%2F%28x%5E2-16%29%2B%282%28x%5E2-8x%2B16%29%29%2F%28x%5E2-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x-4%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B16 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B16\"   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=%2816%29%2F%28x%5E2-16%29%2B%282x%5E2-16x%2B32%29%2F%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"%2816%29%2F%28x%5E2-16%29%2B%282x%5E2-16x%2B32%29%2F%28x%5E2-16%29\"   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=%28%2816%29%2B%282x%5E2-16x%2B32%29%29%2F%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"%28%2816%29%2B%282x%5E2-16x%2B32%29%29%2F%28x%5E2-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since the two fractions have the same denominator, this means we can combine them.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2-16x%2B48%29%2F%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"%282x%5E2-16x%2B48%29%2F%28x%5E2-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2-16x%2B48%29%2F%28x%5E2-16%29 ALIGN=MIDDLE  ALT=\"%282x%5E2-16x%2B48%29%2F%28x%5E2-16%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=%2816%29%2F%28x%5E2-16%29%2B%282%28x-4%29%29%2F%28x%2B4%29=%282x%5E2-16x%2B48%29%2F%28x%5E2-16%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-4 ALIGN=MIDDLE  ALT=\"x%3C%3E-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E4 ALIGN=MIDDLE  ALT=\"x%3C%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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