document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081665>Question 1081665</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify (n+5)!/(n+3)! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695716 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=695716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By definition, \r<BR>\n" );
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document.write( "n! = n*(n-1)*(n-2)*...*3*2*1\r<BR>\n" );
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document.write( "Whatever value you pick for n, you count your way down til you get to 1. All of the integers in the countdown are multiplied.\r<BR>\n" );
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document.write( "Using similar logic, the expression (n+5)! can be expanded as such\r<BR>\n" );
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document.write( "(n+5)! = (n+5)*(n+4)*<font color=red>(n+3)*(n+2)*(n+1)*...*3*2*1</font>\r<BR>\n" );
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document.write( "and that can be turned into\r<BR>\n" );
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document.write( "(n+5)! = (n+5)*(n+4)*<font color=red>(n+3)!</font>\r<BR>\n" );
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document.write( "notice how the red portions match up. They are equal expressions. In other words,\r<BR>\n" );
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document.write( "(n+3)! = (n+3)*(n+2)*(n+1)*...*3*2*1\r<BR>\n" );
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document.write( "Let's use that idea to simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%2B5%29%21%29%2F%28%28n%2B3%29%21%29=%28%28n%2B5%29%28n%2B4%29%28n%2B3%29%21%29%2F%28%28n%2B3%29%21%29 ALIGN=MIDDLE   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%28n%2B5%29%21%29%2F%28%28n%2B3%29%21%29=%28n%2B5%29%28n%2B4%29 ALIGN=MIDDLE  ALT=\"%28%28n%2B5%29%21%29%2F%28%28n%2B3%29%21%29=%28n%2B5%29%28n%2B4%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%28n%2B5%29%21%29%2F%28%28n%2B3%29%21%29=n%5E2%2B9n%2B20 ALIGN=MIDDLE  ALT=\"%28%28n%2B5%29%21%29%2F%28%28n%2B3%29%21%29=n%5E2%2B9n%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Final Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B9n%2B20 ALIGN=MIDDLE  ALT=\"n%5E2%2B9n%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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