document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164558>Question 1164558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the rational inequality. Express answer using interval notation (show work)\r<BR>\n" );
document.write( "\n" );
document.write( "x^2-x-12<BR>\n" );
document.write( "_________>0 <BR>\n" );
document.write( "x^2+x-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788976 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=788976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your inequality is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^2 - x - 12)/(x^2 + x - 6) > 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor these quadratics to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-4)*(x+3)/((x-2)*(x+3)) > 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the (x+3) in the numerator and the denominator cancel out and you are left with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-4)/(x-2) > 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this will be positive when x is greater than 4 or when x is smaller than 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it till be negative when x is > 2 and < 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x is greater than 4, you have a positive numerator divided by a positive denominator which results in a positive number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x is less than 2, you have a negative numerator divided by a negative denominator which results in a positive number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x is greater than 2 and less than 4, you have a negative numerator divided by a positive denominator which results in a negative number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can be seen in the following graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/090904.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the shaded area is when the resulting number is positive.<BR>\n" );
document.write( "the non-shaded area is when the resulting number if negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );