document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=315558>Question 315558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!<BR>\n" );
document.write( "Perform the indicated operations and simplify<BR>\n" );
document.write( "v-7/v-9 - v+1/v+9 + v-45/v^2-81 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225773 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=225773\">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=%28v-7%29%2F%28v-9%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28v%5E2-81%29 ALIGN=MIDDLE  ALT=\"%28v-7%29%2F%28v-9%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28v%5E2-81%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=%28v-7%29%2F%28v-9%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28%28v-9%29%28v%2B9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the last denominator.\r<BR>\n" );
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document.write( "Take note that the LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28v-9%29%28v%2B9%29 ALIGN=MIDDLE  ALT=\"%28v-9%29%28v%2B9%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%28v-7%29%2F%28v-9%29%29%28%28v%2B9%29%2F%28v%2B9%29%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28%28v-9%29%28v%2B9%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=%28v%2B9%29%2F%28v%2B9%29 ALIGN=MIDDLE  ALT=\"%28v%2B9%29%2F%28v%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get that denominator to equal the LCD.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28v-7%29%28v%2B9%29%29%2F%28%28v-9%29%28v%2B9%29%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28%28v-9%29%28v%2B9%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=%28v%5E2%2B2v-63%29%2F%28%28v-9%29%28v%2B9%29%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28%28v-9%29%28v%2B9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL the numerator of the first fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28v%5E2%2B2v-63%29%2F%28%28v-9%29%28v%2B9%29%29+-+%28%28v%2B1%29%2F%28v%2B9%29%29%28%28v-9%29%2F%28v-9%29%29+%2B+%28v-45%29%2F%28%28v-9%29%28v%2B9%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=%28v-9%29%2F%28v-9%29 ALIGN=MIDDLE  ALT=\"%28v-9%29%2F%28v-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get that denominator to equal the LCD.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28v%5E2%2B2v-63%29%2F%28%28v-9%29%28v%2B9%29%29+-+%28%28v%2B1%29%28v-9%29%29%2F%28%28v%2B9%29%28v-9%29%29+%2B+%28v-45%29%2F%28%28v-9%29%28v%2B9%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=%28v%5E2%2B2v-63%29%2F%28%28v-9%29%28v%2B9%29%29+-+%28v%5E2-8v-9%29%2F%28%28v%2B9%29%28v-9%29%29+%2B+%28v-45%29%2F%28%28v-9%29%28v%2B9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL the numerator of the second fraction.\r<BR>\n" );
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document.write( "Now the denominators are all equal to the LCD, we can finally combine the three fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28v%5E2%2B2v-63%29-+%28v%5E2-8v-9%29%2B+%28v-45%29%29%2F%28%28v-9%29%28v%2B9%29%29 ALIGN=MIDDLE  ALT=\"%28%28v%5E2%2B2v-63%29-+%28v%5E2-8v-9%29%2B+%28v-45%29%29%2F%28%28v-9%29%28v%2B9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the three fractions by placing the numerators all over the LCD.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28v%5E2%2B2v-63-+v%5E2%2B8v%2B9%2Bv-45%29%2F%28%28v-9%29%28v%2B9%29%29 ALIGN=MIDDLE  ALT=\"%28v%5E2%2B2v-63-+v%5E2%2B8v%2B9%2Bv-45%29%2F%28%28v-9%29%28v%2B9%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=%2811v-99%29%2F%28%28v-9%29%28v%2B9%29%29 ALIGN=MIDDLE  ALT=\"%2811v-99%29%2F%28%28v-9%29%28v%2B9%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=%2811%28v-9%29%29%2F%28%28v-9%29%28v%2B9%29%29 ALIGN=MIDDLE  ALT=\"%2811%28v-9%29%29%2F%28%28v-9%29%28v%2B9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the numerator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2Ahighlight%28%28v-9%29%29%29%2F%28highlight%28%28v-9%29%29%28v%2B9%29%29 ALIGN=MIDDLE  ALT=\"%2811%2Ahighlight%28%28v-9%29%29%29%2F%28highlight%28%28v-9%29%29%28v%2B9%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=%2811%2Across%28%28v-9%29%29%29%2F%28cross%28%28v-9%29%29%28v%2B9%29%29 ALIGN=MIDDLE  ALT=\"%2811%2Across%28%28v-9%29%29%29%2F%28cross%28%28v-9%29%29%28v%2B9%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=11%2F%28v%2B9%29 ALIGN=MIDDLE  ALT=\"11%2F%28v%2B9%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=%28v-7%29%2F%28v-9%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28v%5E2-81%29 ALIGN=MIDDLE  ALT=\"%28v-7%29%2F%28v-9%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28v%5E2-81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F%28v%2B9%29 ALIGN=MIDDLE  ALT=\"11%2F%28v%2B9%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=%28v-7%29%2F%28v-9%29+-+%28v%2B1%29%2F%28v%2B9%29+%2B+%28v-45%29%2F%28v%5E2-81%29=11%2F%28v%2B9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%3C%3E-9 ALIGN=MIDDLE  ALT=\"v%3C%3E-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%3C%3E9 ALIGN=MIDDLE  ALT=\"v%3C%3E9\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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