document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135174>Question 1135174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I done the following rational expression addition and subtraction 4*x/(x^2-1)+3*x/(1-x)-4/(x-1) and had some issues with it , I have seen the full answer and got stuck on how some things were arrived at . I wonder if some one would kindly shed some light on the following. 1, in  both the second term -3*x/1-x and third term  -4/(x-1) could a greater explanation of how or why the denominators are allocated to there numerators? I would have thought that the  third term -4/(x-1) would equal -4*(-x+1)*(x+1)/(x+1)*(-x+1)*(x-1) instead of -4*(x+1)*(x-1) ?  2, and finally an explanation of how factoring the total numerator is achieved ?  As all this would be much appreciated kind regards mike. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752744 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "It appears that you are trying to use<br><BR>\n" );
document.write( "(x+1)(x-1)(-x+1)<br><BR>\n" );
document.write( "as your common denominator.<br><BR>\n" );
document.write( "What you are overlooking is the fact that<br><BR>\n" );
document.write( "(-x+1) = -1(x-1)<br><BR>\n" );
document.write( "So you don't need both (x-1) and (-x+1) in your common denominator.<br><BR>\n" );
document.write( "You will be seeing a lot of problems in which expressions like (2x-3) and (-2x+3) appear.  Learn to recognize that kind of thing.<br><BR>\n" );
document.write( "Also, in general, when working with polynomials of any size, it is always far more awkward if any of the leading coefficients are negative.<br><BR>\n" );
document.write( "So in a problem like this, where you have terms of<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2F%281-x%29 ALIGN=MIDDLE  ALT=\"3x%2F%281-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"-4%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "rewrite the first one by multiplying top and bottom by -1, making it<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"-3x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then you will see that the common denominator you want to use is simply (x+1)(x-1).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2F%28x%5E2-1%29+%2B+3x%2F%281-x%29+-+4%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"4x%2F%28x%5E2-1%29+%2B+3x%2F%281-x%29+-+4%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2F%28x%5E2-1%29+-+3x%2F%28x-1%29+-+4%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"4x%2F%28x%5E2-1%29+-+3x%2F%28x-1%29+-+4%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2F%28x%5E2-1%29+-+%283x%29%28x%2B1%29%2F%28%28x-1%29%28x%2B1%29%29+-+%284%29%28x%2B1%29%2F%28%28x-1%29%28x%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since that's the specific part of the problem you asked about, I'll leave my response there and assume that you can finish simplifying the expression. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );