document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148489>Question 148489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x+9/x^2-9)-(2/x-3)<BR>\n" );
document.write( "It has been 4 years since I graduated highschool and I'm having trouble remembering how to do this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108817 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=108817\">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=%28x%2B9%29%2F%28x%5E2-9%29-%282%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%2F%28x%5E2-9%29-%282%29%2F%28x-3%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=%28x%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%282%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%282%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-9 ALIGN=MIDDLE  ALT=\"x%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (use the difference of squares)\r<BR>\n" );
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document.write( "In order to add or subtract any fractions, we need to have <font size=4><b>every</b></font> denominator to be the same. So we need to have <font size=4><b>every</b></font> denominator equal to the LCD. In this case, the LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-3%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%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%28%282%29%2F%28x-3%29%29%28%28x%2B3%29%2F%28x%2B3%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%2B3%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Doing this will make the second fraction have a denominator equal to the LCD.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%282%28x%2B3%29%29%2F%28%28x%2B3%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%282%28x%2B3%29%29%2F%28%28x%2B3%29%28x-3%29%29\"   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%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%282x%2B6%29%2F%28%28x%2B3%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%282x%2B6%29%2F%28%28x%2B3%29%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "Now that we have equal denominators, we can 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%2B9-%282x%2B6%29%29%2F%28%28x%2B3%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B9-%282x%2B6%29%29%2F%28%28x%2B3%29%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the numerators over the common denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B9-2x-6%29%2F%28%28x%2B3%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B9-2x-6%29%2F%28%28x%2B3%29%28x-3%29%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-x%2B3%29%2F%28%28x%2B3%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28-x%2B3%29%2F%28%28x%2B3%29%28x-3%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=%28-%28x-3%29%29%2F%28%28x%2B3%29%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28-%28x-3%29%29%2F%28%28x%2B3%29%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor a -1 from the numerator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-highlight%28%28x-3%29%29%29%2F%28%28x%2B3%29highlight%28%28x-3%29%29%29 ALIGN=MIDDLE  ALT=\"%28-highlight%28%28x-3%29%29%29%2F%28%28x%2B3%29highlight%28%28x-3%29%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=%28-cross%28%28x-3%29%29%29%2F%28%28x%2B3%29cross%28%28x-3%29%29%29 ALIGN=MIDDLE  ALT=\"%28-cross%28%28x-3%29%29%29%2F%28%28x%2B3%29cross%28%28x-3%29%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=%28-1%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28x%2B3%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=%28x%2B9%29%2F%28x%5E2-9%29-%282%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%2F%28x%5E2-9%29-%282%29%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28x%2B3%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=%28x%2B9%29%2F%28x%5E2-9%29-%282%29%2F%28x-3%29=%28-1%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%2F%28x%5E2-9%29-%282%29%2F%28x-3%29=%28-1%29%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-3 ALIGN=MIDDLE  ALT=\"x%3C%3E-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E3 ALIGN=MIDDLE  ALT=\"x%3C%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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