document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278468>Question 278468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help simplifying complex rational expression I tried method 2 w/lcd\r<BR>\n" );
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document.write( " x-4/x-1 - x/x-3<BR>\n" );
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document.write( "3+ 12/x-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202700 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</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=202700\">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%28x-4%29%2F%28x-1%29+-+x%2F%28x-3%29%29%2F%283%2B+12%2F%28x-3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-4%29%2F%28x-1%29+-+x%2F%28x-3%29%29%2F%283%2B+12%2F%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The LCD of all the \"little\" fractions is the right approach. The LCD here is:<BR>\n" );
document.write( "(x-1)(x-3)<BR>\n" );
document.write( "Multiplying the numerator and denominator of the \"big\" fraction by the LCD we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x-4%29%2F%28x-1%29+-+x%2F%28x-3%29%29%2F%283%2B+12%2F%28x-3%29%29%29%28%28x-1%29%28x-3%29%2F%28x-1%29%28x-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To multiply this we need to use the Distributive Property on both the numerator and denominator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-1%29%28x-3%29%28%28x-4%29%2F%28x-1%29%29+-+%28x-1%29%28x-3%29%28x%2F%28x-3%29%29%29%2F%28%28x-1%29%28x-3%293%2B+%28x-1%29%28x-3%29%2812%2F%28x-3%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can start canceling:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28%28x-1%29%29%28x-3%29%28%28x-4%29%2Fcross%28%28x-1%29%29%29+-+%28x-1%29cross%28%28x-3%29%29%28x%2Fcross%28%28x-3%29%29%29%29%2F%28%28x-1%29%28x-3%293%2B+%28x-1%29cross%28%28x-3%29%29%2812%2Fcross%28%28x-3%29%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=%28%28x-3%29%28x-4%29+-+%28x-1%29%28x%29%29%2F%28%28x-1%29%28x-3%293%2B+%28x-1%29%2812%29%29 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%28x-4%29+-+%28x-1%29%28x%29%29%2F%28%28x-1%29%28x-3%293%2B+%28x-1%29%2812%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can finally multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2+-+7x+%2B12%29+-+%28x%5E2+-+x%29%29%2F%28%283x%5E2+-12x+%2B+9%29+%2B+%2812x+-+12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combining like terms we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6x+%2B+12%29%2F%283x%5E2+-+3%29 ALIGN=MIDDLE  ALT=\"%28-6x+%2B+12%29%2F%283x%5E2+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can reduce the fraction. To reduce fractions you cancel factors which are common to the numerator and denominator. So we need factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-6%28x+-2%29%29%2F%283%28x%5E2+-+1%29%29 ALIGN=MIDDLE  ALT=\"%28-6%28x+-2%29%29%2F%283%28x%5E2+-+1%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=%28-6%28x+-2%29%29%2F%283%28x%2B1%29%28x+-+1%29%29 ALIGN=MIDDLE  ALT=\"%28-6%28x+-2%29%29%2F%283%28x%2B1%29%28x+-+1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A factor of 3 will cancel:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%28x+-2%29%29%2F%28%28x%2B1%29%28x+-+1%29%29 ALIGN=MIDDLE  ALT=\"%28-2%28x+-2%29%29%2F%28%28x%2B1%29%28x+-+1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "No more reducing is possible so we'll multiply out the top and bottom:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2x%2B4%29%2F%28x%5E2+-1%29 ALIGN=MIDDLE  ALT=\"%28-2x%2B4%29%2F%28x%5E2+-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );