document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=486610>Question 486610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Appreciate help in solving a problem and checking the answer:\r<BR>\n" );
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document.write( "((6x-3)/x^2-x-12))-((2x-15)/x^2-x-12))\r<BR>\n" );
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document.write( "The answer I got is 4/(x-4) but not sure if this is correct and don't know how to check.\r<BR>\n" );
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document.write( "Thanks much.\r<BR>\n" );
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document.write( "Diane </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332625 by </B><A HREF=/tutors/aboutme.mpl?userid=chessace><B>chessace(471)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chessace><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=chessace><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=332625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since () are used somewhat, assume (1st) this problem is<BR>\n" );
document.write( "((6x-3)/x^2)-x-12-((2x-15)/x^2)-x-12 rather than<BR>\n" );
document.write( "(2nd) (6x-3)/(x^2-x-12)-(2x-15)/(x^2-x-12).<BR>\n" );
document.write( "Maybe it was clear in original form.<BR>\n" );
document.write( "(1st):<BR>\n" );
document.write( "((6x-3)/x^2)-x-12-((2x-15)/x^2)-x-12<BR>\n" );
document.write( "= ((6x-3-2x+15)/x^2)-x-12-x-12<BR>\n" );
document.write( "= ((4x+12)/x^2) -2(4x+12) not looking good!<BR>\n" );
document.write( "(2nd):<BR>\n" );
document.write( "(6x-3)/(x^2-x-12)-(2x-15)/(x^2-x-12)<BR>\n" );
document.write( "= (6x-3-2x+15)/(x^2-x-12)<BR>\n" );
document.write( "= (4x+12)/((x+3)(x-4))<BR>\n" );
document.write( "= 4/(x-4)<BR>\n" );
document.write( "Much better, and matches yours.<BR>\n" );
document.write( "As for checking any answer, one quick test is to set x=0 then x=1 and see if results are same:<BR>\n" );
document.write( "x=0: -3/(-12)-(-15)/(-12)= 1/4-5/4 = -1 v. -1 OK!<BR>\n" );
document.write( "x=1: (3/-12)-(-13)/(-12) = -1/4 - 13/12 v. 4/(-3)<BR>\n" );
document.write( "(-3/12)-13/12 v. -16/12 OK!<BR>\n" );
document.write( "A 3rd point, say x=-1 would cinch it, but 2 is plenty.<BR>\n" );
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