document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85478>Question 85478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> n^2-9-20/2n^2 x n^2+5n/n^2-25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61743 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=61743\">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=%28%28n%5E2+-+9%2An+%2B+20%29%2F%282%2An%5E2%29%29%2A%28%28n%5E2+%2B+5%2An%29%2F%28n%5E2+-+25%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression (note: it should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+-+9%2An+%2B+20 ALIGN=MIDDLE  ALT=\"n%5E2+-+9%2An+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2+-+9%2An+-+20 ALIGN=MIDDLE  ALT=\"n%5E2+-+9%2An+-+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28n-4%29%28n-5%29%29%2F%282%2An%5E2%29%29%2A%28%28n%5E2+%2B+5%2An%29%2F%28n%5E2+-+25%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the first numerator (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/quadratic-factoring.solver>solver</a>)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28n-4%29%28n-5%29%29%2F%282n%5E2%29%29%2A%28%28n%28n%2B5%29%29%2F%28n%5E2+-+25%29%29 ALIGN=MIDDLE  ALT=\"%28%28%28n-4%29%28n-5%29%29%2F%282n%5E2%29%29%2A%28%28n%28n%2B5%29%29%2F%28n%5E2+-+25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the second numerator \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28n-4%29%28n-5%29%29%2F%282n%5E2%29%29%2A%28%28n%28n%2B5%29%29%2F%28%28n%2B5%29%28n-5%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the second denominator \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28n-4%29highlight%28%28n-5%29%29%29%2F%282%2An%5E2%29%29%2A%28%28n%2Ahighlight%28%28n%2B5%29%29%2F%28highlight%28%28n%2B5%29%29highlight%28%28n-5%29%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Notice we have these common terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28n-4%29cross%28%28n-5%29%29%29%2F%282%2An%5E2%29%29%2A%28%28n%2Across%28%28n%2B5%29%29%2F%28cross%28%28n%2B5%29%29cross%28%28n-5%29%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > They divide and cancel out  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n-4%29%2F%282n%5E2%29%29%28n%2F1%29 ALIGN=MIDDLE  ALT=\"%28%28n-4%29%2F%282n%5E2%29%29%28n%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%5E2 ALIGN=MIDDLE  ALT=\"2n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2n ALIGN=MIDDLE  ALT=\"1%2F2n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-4%29%2F%282n%29 ALIGN=MIDDLE  ALT=\"%28n-4%29%2F%282n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "So the expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%5E2+-+9%2An+%2B+20%29%2F%282%2An%5E2%29%29%2A%28%28n%5E2+%2B+5%2An%29%2F%28n%5E2+-+25%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplifies to\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-4%29%2F%282n%29 ALIGN=MIDDLE  ALT=\"%28n-4%29%2F%282n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As always, we can verify our answer. We can graph the original expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%5E2+-+9%2An+%2B+20%29%2F%282%2An%5E2%29%29%2A%28%28n%5E2+%2B+5%2An%29%2F%28n%5E2+-+25%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "as a function of x and y like this\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+%28%28x%5E2+-+9%2Ax+%2B+20%29%2F%282%2Ax%5E2%29%29%2A%28%28x%5E2+%2B+5%2Ax%29%2F%28x%5E2+-+25%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%28x%5E2+-+9%2Ax+%2B+20%29%2F%282%2Ax%5E2%29%29%2A%28%28x%5E2+%2B+5%2Ax%29%2F%28x%5E2+-+25%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and graph the simplified result\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-4%29%2F%282n%29 ALIGN=MIDDLE  ALT=\"%28n-4%29%2F%282n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C%28x-4%29%2F%282x%29%29 ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C%28x-4%29%2F%282x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-4%29%2F%282x%29 ALIGN=MIDDLE  ALT=\"y=%28x-4%29%2F%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since they produce the same graphs, this means they are equivalent. Since they are equivalent, this means that our answer has been verified.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );