document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=614963>Question 614963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (2x^3+2x)/(x^2-2x)*(x-1)/(4x^2+4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #386833 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3759)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=386833\">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%282x%5E3%2B2x%29%2F%28x%5E2-2x%29%29%2A%28%28x-1%29%2F%284x%5E2%2B4%29%29 ALIGN=MIDDLE  ALT=\"%28%282x%5E3%2B2x%29%2F%28x%5E2-2x%29%29%2A%28%28x-1%29%2F%284x%5E2%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Back in the \"good old days\", when fractions were just made of numbers, you learned:<ul><li>Fractions are reduced by canceling factors that are common to the numerator and the denominator.</li><li>When multiplying fractions...<ul><li>It is not only OK but it is a very good idea to cancel <i>before</i> you multiply</li><li>\"Cross-canceling\" is OK. Cross-canceling is when you cancel a factor of a numerator (or denominator) of one fraction with the same factor in the denominator (or numerator) of another fraction. (You'll see this shortly.)</li></ul></li></ul>The same is true with these fractions! In fact, it is even more important then ever to cancel before you actually multiply!!<br><BR>\n" );
document.write( "So we'll start by canceling factors. And to cancel factors we need to know what the factors are. So we factor the numerators and denominators:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x%28x%5E2%2B1%29%29%2F%28x%28x-2%29%29%29%28%28x-1%29%2F%282%2A2%2A%28x%5E2%2B1%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now that we can see the factors, we can see that there are some factors to cancel, including cross-canceling the 2 and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B1 ALIGN=MIDDLE  ALT=\"x%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28cross%282%29cross%28x%29cross%28%28x%5E2%2B1%29%29%29%2F%28cross%28x%29%28x-2%29%29%29%28%28x-1%29%2F%28cross%282%29%2A2%2Across%28%28x%5E2%2B1%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "leaving<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28x-2%29%29%28%28x-1%29%2F2%29 ALIGN=MIDDLE  ALT=\"%281%2F%28x-2%29%29%28%28x-1%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This, you must agree, is a lot easier to multiply than what we started with. Multiplying we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%282x-4%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%282x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );