document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256883>Question 256883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. (2x^2 + x - 3)/9 times (x + 1)^2/(2x^2 + 5x + 3)\r<BR>\n" );
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document.write( "2. 1/(25 - y^2) divided by (6 - 3y)/y^2 - 7y + 10)\r<BR>\n" );
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document.write( "3. abc/(a^2 - 3a - 10) divided by a^2/(a^2 - 25) times (4 - a^2/9b^2 - 4 divided by (abc + 5bc)/(3ab - 2a)\r<BR>\n" );
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document.write( "4. (n^2 + 5n + 6)/(n^2 + 7n + 12 times (n^2 + 9n + 20/(n^2 + 11n + 30) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188987 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=188987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. (2x^2 + x - 3)/9 times (x + 1)^2/(2x^2 + 5x + 3) <BR>\n" );
document.write( "step 1 - factor all possible polynomials as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+3%29%28x-1%29%2F9 ALIGN=MIDDLE  ALT=\"%282x+%2B+3%29%28x-1%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+1%29%5E2%2F%28%282x%2B3%29%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%5E2%2F%28%282x%2B3%29%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "step 2 - cancel where needed as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-1%29%2F9%29%2A%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28%28x-1%29%2F9%29%2A%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is simplified as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-1%29%2F9 ALIGN=MIDDLE  ALT=\"%28x%5E2-1%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "2. 1/(25 - y^2) divided by (6 - 3y)/y^2 - 7y + 10) <BR>\n" );
document.write( "step 1 - factor all possible polynomials as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%285%2By%29%285-y%29%29 ALIGN=MIDDLE  ALT=\"1%2F%285%2By%29%285-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > /  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%282-y%29%29%2F%28%28y-5%29%28y%2B3%29%29+ ALIGN=MIDDLE  ALT=\"%283%282-y%29%29%2F%28%28y-5%29%28y%2B3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 2 - multiply by reciprocal to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%285%2By%29%285-y%29%29 ALIGN=MIDDLE  ALT=\"1%2F%285%2By%29%285-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-5%29%28y%2B3%29%29%2F%283%282-y%29%29%7D%7D%0D%0Astep+3+-+cancel+where+needed+as%0D%0A%7B%7B%7B-1%2F%28y%2B5%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B3%29%2F%283%2A%282-y%29%29 ALIGN=MIDDLE  ALT=\"%28y%2B3%29%2F%283%2A%282-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28y%2B3%29%2F%28-3y%5E2-3y%2B10%29 ALIGN=MIDDLE  ALT=\"-%28y%2B3%29%2F%28-3y%5E2-3y%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "3. abc/(a^2 - 3a - 10) divided by a^2/(a^2 - 25) times (4 - a^2/9b^2 - 4 divided by (abc + 5bc)/(3ab - 2a) <BR>\n" );
document.write( "step 1 - factor all possible polynomials<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abc%2F%28%28a-5%29%28a%2B2%29%29 ALIGN=MIDDLE  ALT=\"abc%2F%28%28a-5%29%28a%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > / <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2F%28%28a%2B5%29%28a-5%29%29 ALIGN=MIDDLE  ALT=\"a%5E2%2F%28%28a%2B5%29%28a-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ba%29%282-a%29%2F%28%283b%2B2%29%283b-2%29%29 ALIGN=MIDDLE  ALT=\"%282%2Ba%29%282-a%29%2F%28%283b%2B2%29%283b-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > / <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bc%28a%2B5%29%2F%283b-2a%29 ALIGN=MIDDLE  ALT=\"bc%28a%2B5%29%2F%283b-2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abc%2F%28%28a-5%29%28a%2B2%29%29 ALIGN=MIDDLE  ALT=\"abc%2F%28%28a-5%29%28a%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28a%2B5%29%28a-5%29%29%2Fa%5E2 ALIGN=MIDDLE  ALT=\"%28%28a%2B5%29%28a-5%29%29%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283b-2a%29%2Fbc%28a%2B5%29 ALIGN=MIDDLE  ALT=\"%283b-2a%29%2Fbc%28a%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ba%29%282-a%29%2F%28%283b%2B2%29%283b-2%29%29 ALIGN=MIDDLE  ALT=\"%282%2Ba%29%282-a%29%2F%28%283b%2B2%29%283b-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 2 - reduce as needed to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B5%29%282-a%29%283b-2a%29 ALIGN=MIDDLE  ALT=\"%28a%2B5%29%282-a%29%283b-2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > / <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%283b%2B2%29%283b-2%29 ALIGN=MIDDLE  ALT=\"a%283b%2B2%29%283b-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "4. (n^2 + 5n + 6)/(n^2 + 7n + 12 times (n^2 + 9n + 20/(n^2 + 11n + 30)<BR>\n" );
document.write( "step 1  -factor all possible polynomials to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%2B3%29%28n%2B2%29%29%2F%28%28n%2B3%29%28n%2B4%29%29 ALIGN=MIDDLE  ALT=\"%28%28n%2B3%29%28n%2B2%29%29%2F%28%28n%2B3%29%28n%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%2B4%29%28n%2B5%29%29%2F%28%28n%2B5%29%28n%2B6%29%29 ALIGN=MIDDLE  ALT=\"%28%28n%2B4%29%28n%2B5%29%29%2F%28%28n%2B5%29%28n%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this reduces nicely to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B2%29%2F%28n%2B6%29 ALIGN=MIDDLE  ALT=\"%28n%2B2%29%2F%28n%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );