document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=718129>Question 718129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the following expressions.\r<BR>\n" );
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document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28m%281%2F%28m%5E2-4%29%29%29%2F%281%2F%28m%2B2%29%29+ ALIGN=MIDDLE  ALT=\"+%28m%281%2F%28m%5E2-4%29%29%29%2F%281%2F%28m%2B2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28ac%2Bad%2Bbc%2Bbd%29%2F%28a%5E2-b%5E2%29%29%28%28a%5E3-b%5E3%29%2F%282a%5E2%2B2ab%2B2b%5E2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440833 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=440833\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In (a) you invert and multiply to get<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%281%2F%28m%5E2-4%29%29%2A%28m%2B2%29 ALIGN=MIDDLE  ALT=\"m%281%2F%28m%5E2-4%29%29%2A%28m%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Now factor<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%5E2-4%29+=+%28m%2B2%29%2A%28m-2%29 ALIGN=MIDDLE  ALT=\"%28m%5E2-4%29+=+%28m%2B2%29%2A%28m-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and put into (1) and get<BR>\n" );
document.write( "(3) (a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2F%28m-2%29 ALIGN=MIDDLE  ALT=\"m%2F%28m-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For (b) we need to factor all four polynomials.<BR>\n" );
document.write( "First one<BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ac+%2Bad+%2Bbc+%2Bbd%29+=+a%28c%2Bd%29+%2Bb%28c%2Bd%29 ALIGN=MIDDLE  ALT=\"%28ac+%2Bad+%2Bbc+%2Bbd%29+=+a%28c%2Bd%29+%2Bb%28c%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "(5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ac+%2Bad+%2Bbc+%2Bbd%29+=+%28a%2Bb%29%2A%28c%2Bd%29 ALIGN=MIDDLE  ALT=\"%28ac+%2Bad+%2Bbc+%2Bbd%29+=+%28a%2Bb%29%2A%28c%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Second one<BR>\n" );
document.write( "(6) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2+=+%28a%2Bb%29%2A%28a-b%29 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2+=+%28a%2Bb%29%2A%28a-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Third one<BR>\n" );
document.write( "(7) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3-b%5E3%29+=+%28a-b%29%2A%28a%5E2%2Bab%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"%28a%5E3-b%5E3%29+=+%28a-b%29%2A%28a%5E2%2Bab%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Fourth one<BR>\n" );
document.write( "(8) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282a%5E2%2B2ab%2B2b%5E2%29+=+2%2A%28a%5E2%2Bab%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"%282a%5E2%2B2ab%2B2b%5E2%29+=+2%2A%28a%5E2%2Bab%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Replacing each polynomial of b) with its factored form and cancelling like factors yields<BR>\n" );
document.write( "(9) (b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%2Bd%29%2F2 ALIGN=MIDDLE  ALT=\"%28c%2Bd%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );