document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977750>Question 977750</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, the question asks to simplify the following algebraic expression. I apologize if this isn't the correct topic I have selected. The question is: \"Simplify the following algebraic expression:((x+1)^3 (3x-5) - (x+1)^2 (8x+3))/(x-4)(x+1)^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599331 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=599331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ((x+1)^3 (3x-5) - (x+1)^2 (8x+3))/(x-4)(x+1)^3=\r<BR>\n" );
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document.write( "((x+1)^3)(3x-5))/(x-4) (x+1)^3     minus     (x+1)^2(8x+3)/(x-4) (x+1)^3.   Split the fraction.\r<BR>\n" );
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document.write( "Cancel the (x+1)^3 completely in the first numerator term and (x+1)^2 in the second term.\r<BR>\n" );
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document.write( "This leaves <BR>\n" );
document.write( "[(3x-5)/(x-4)]  - ((8x+3)/(x+1)\r<BR>\n" );
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document.write( "common denominator is (x-4)(x+1)<BR>\n" );
document.write( "numerator will be (3x-5)(x+1)=3x^2-17x20  -  [8x+3)(x-4)]<BR>\n" );
document.write( "second part is 8x^2-29x-12,<BR>\n" );
document.write( "3x^2-17x+20-8x^2+29x+12= {-5x^2+12x+32}/(x-4)(x+1)=  -(5x^2-12x-32)/(x-4)(x+1)=<BR>\n" );
document.write( "-(5x+8)(x-4)/(x-4)(x+1)= -(5x+8)/(x+1), because the (x-4) divide out.\r<BR>\n" );
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document.write( "Notice that I pull a minus sign out of the equation, because factoring -x^2 terms is difficult.\r<BR>\n" );
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document.write( "Do not multiply out the numerator at first.  Split it into two fractions, cancel what you can, then put everything over a common denominator and simplify that.  Often you can cancel further.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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