document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121667>Question 1121667</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't know how to start this.<BR>\n" );
document.write( "2/x+3 -  1/x+1 < 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737625 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2/(x+3) - 1/(x+1) < 0\r<BR>\n" );
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document.write( "this function is undefined when x = -3 and when x = -1.\r<BR>\n" );
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document.write( "this function is equal to 0 when x = 1.\r<BR>\n" );
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document.write( "to solve for that, set the function equal to 0.\r<BR>\n" );
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document.write( "you get 2/(x+3) - 1/(x+1) = 0\r<BR>\n" );
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document.write( "multiply both sides of the equiation by (x+3) * (x+1) to get:\r<BR>\n" );
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document.write( "2 * (x+1) - (x + 3) = 0\r<BR>\n" );
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document.write( "simplify to get 2x + 2 - x - 3 = 0\r<BR>\n" );
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document.write( "combine like terms to get x - 1 = 0\r<BR>\n" );
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document.write( "solve for x to get x = 1\r<BR>\n" );
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document.write( "you have 4 intervals that need to be checked.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "x < -3<BR>\n" );
document.write( "x between -3 and -1<BR>\n" );
document.write( "x between -1 and 1<BR>\n" );
document.write( "x > 1\r<BR>\n" );
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document.write( "the function is continuous between these intervals.<BR>\n" );
document.write( "therefore, within each interval, if it is greater than 0, it stays greater than 0 and, if it is less than 0, it says less than 0.\r<BR>\n" );
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document.write( "it can only go from positive to negative at either side of the vertical asymptotes or when x = 1.\r<BR>\n" );
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document.write( "the function is 2/(x+3) - 1/(x+1) < 0\r<BR>\n" );
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document.write( "when x = -4,  the function is 2/-1 - 1/-3 = -2 + 1/3 = less than 0.\r<BR>\n" );
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document.write( "when x = -2, the function is 2/1 - 1/-1 = 2 + 1 = greater than 0.\r<BR>\n" );
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document.write( "when x = 0, the function is 2/3 - 1 = less than 0.\r<BR>\n" );
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document.write( "when x = 2, the function is 2/5 - 1/3 = greater than 0.\r<BR>\n" );
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document.write( "it appears that the function is less than 0 when x < -3 and when x is between -1 and 1.\r<BR>\n" );
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document.write( "the following graph confirms that.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/082301.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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