document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172045>Question 172045</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm not sure how to work this could someone help me please.<BR>\n" );
document.write( "11/x^2-4-8/x+2  (/= over)directions are subtract and simplify if possible. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127078 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think that the expression you were trying to render looks something like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2F%28x%5E2-4%29%29-%288%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%2811%2F%28x%5E2-4%29%29-%288%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And I will proceed on that basis.\r<BR>\n" );
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document.write( "In order to subtract fractions, you need a common denominator.  You can always find a common denominator simply by multiplying all of your denominators together, but if your denominators have common factors, you can create a Lowest Common Denominator (LCD) that will simplify your work.\r<BR>\n" );
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document.write( "But what factor(s) do <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > have in common?  Look closely at your first denominator.  Do you recognize the 'difference of two squares' pattern?  Do you recall from your study of factoring quadratic polynomials the rule for factoring the difference of two squares?\r<BR>\n" );
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document.write( "Remember: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2=%28a%2Bb%29%28a-b%29 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2=%28a%2Bb%29%28a-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Therfore:  <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;\" >.\r<BR>\n" );
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document.write( "But look:  Now you can see that <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > have the factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in common.  Hence, the LCD is simply <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;\" >.\r<BR>\n" );
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document.write( "Let's apply the common denominator to the original expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2F%28x%5E2-4%29%29-%288%28x-2%29%2F%28x%2B2%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%2811%2F%28x%5E2-4%29%29-%288%28x-2%29%2F%28x%2B2%29%28x-2%29%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=%2811%2F%28x%5E2-4%29%29-%288%28x-2%29%2F%28x%5E2-4%29%29%29 ALIGN=MIDDLE  ALT=\"%2811%2F%28x%5E2-4%29%29-%288%28x-2%29%2F%28x%5E2-4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute, collect like terms, and add the numerators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811-8x%2B16%29%2F%28x%5E2-4%29%29%29 ALIGN=MIDDLE  ALT=\"%2811-8x%2B16%29%2F%28x%5E2-4%29%29%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=%2827-8x%29%2F%28x%5E2-4%29%29%29 ALIGN=MIDDLE  ALT=\"%2827-8x%29%2F%28x%5E2-4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Done </SPAN>\n" );
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