document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29250>Question 29250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone pls help me with Simplifying Rational Expressions?, thanks!\r<BR>\n" );
document.write( "\n" );
document.write( "1) <a  rel=nofollow HREF=\"http://photobucket.com\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://i10.photobucket.com/albums/a139/mzzunderstood/untitled4.jpg\" border=\"0\" alt=\"Image hosting by Photobucket\"></a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2) <a  rel=nofollow HREF=\"http://photobucket.com\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://i10.photobucket.com/albums/a139/mzzunderstood/untitled1.jpg\" border=\"0\" alt=\"Image hosting by Photobucket\"></a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3) <a  rel=nofollow HREF=\"http://photobucket.com\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://i10.photobucket.com/albums/a139/mzzunderstood/untitled6.jpg\" border=\"0\" alt=\"Image hosting by Photobucket\"></a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16075 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=16075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can someone pls help me with Simplifying Rational Expressions?, thanks! \r<BR>\n" );
document.write( "\n" );
document.write( "1) (3a^2+15a)/(a^3-25a)<BR>\n" );
document.write( "= [3a(a+5)]/[a(a^2-5^2)]   <BR>\n" );
document.write( "=3(a+5)/[(a+5)(a-5)]  (canceling a)<BR>\n" );
document.write( "(using formula (a^2-b^2)= (a+b)(a-b), here a is a and b =5)<BR>\n" );
document.write( "=3/(a-5)(canceling(a+5)<BR>\n" );
document.write( "Answer:(3a^2+15a)/(a^3-25a)=3/(a-5)\r<BR>\n" );
document.write( "\n" );
document.write( "2)(2x^2-14x)/(x^2-10x+21)<BR>\n" );
document.write( "=[2x(x-7)]/[(x-7)(x-3)]<BR>\n" );
document.write( "=2x/(x-3)  (cancel.. (x-7)<BR>\n" );
document.write( "Answer:(2x^2-14x)/(x^2-10x+21)= 2x/(x-3)<BR>\n" );
document.write( "Note: Since the nr contains the factor (x-7), usually the trick of assuming one factor in the dr as (x-7) and later trying the next factor and see if it works is one of the short cuts that will  work at times!<BR>\n" );
document.write( "Note: (x^2-10x+21)<BR>\n" );
document.write( "= x^2+(-7x-3x)+21  <BR>\n" );
document.write( "= (x^2-7x)-3x+21 <BR>\n" );
document.write( "= x(x-7)-3x+21 <BR>\n" );
document.write( "= x(x-7)-3(x-7)<BR>\n" );
document.write( "=xp-3p Where p=(x-7)<BR>\n" );
document.write( "=p(x-3)<BR>\n" );
document.write( "= (x-7)(x-3)    <BR>\n" );
document.write( "[(splitting the middle term as a sum of two terms in such a way that their product is the product of the square term and the constant term)<BR>\n" );
document.write( "And so, -10x = (-7x) +(-3x) and (-7x)X(-3x) = +21x^2 = (x^2)X(21)]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3) (1-3x)/(3x^2+14x-5)<BR>\n" );
document.write( "=(1-3x)/[(x+5)(3x-1)]<BR>\n" );
document.write( "=-(3x-1)/[(x+5)(3x-1)]<BR>\n" );
document.write( "(pulling out (-1) in the nr so as to get (3x-1) same as that in the dr)<BR>\n" );
document.write( "=-1/(x+5)  (cancel..(3x-1) )<BR>\n" );
document.write( "Answer:(1-3x)/(3x^2+14x-5)=-1/(x+5)  <BR>\n" );
document.write( "Note: take the quadratic expression (3x^2+14x-5)in the rough work column <BR>\n" );
document.write( "and factorise it as follows:<BR>\n" );
document.write( "(3x^2+14x-5)<BR>\n" );
document.write( "=3x^2+(15x-x)-5 <BR>\n" );
document.write( "splitting the middle term as a sum of two terms in such a way that their product is the product of the square term and the constant term)<BR>\n" );
document.write( "And so, 14x = (15x)+(-x) so that (15x)X(-x) = -15x^2 = (3x^2)X(-5)<BR>\n" );
document.write( "=(3x^2+15x)-x-5<BR>\n" );
document.write( "=3x(x+5)-1(x+5)<BR>\n" );
document.write( "=3xp-p where p= (x+5)<BR>\n" );
document.write( "=p(3x-1)<BR>\n" );
document.write( "=(x+5)(3x-1) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );