document.write( "Question 1164558: Solve the rational inequality. Express answer using interval notation (show work)\r
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Algebra.Com's Answer #788974 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "Solve the rational inequality. Express answer using interval notation (show work)
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document.write( "The numerator   x^2-x-12 = (x-4)*(x+3).\r\n" );
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document.write( "The denominator x^2+x-6  = (x-2)*(x+3).\r\n" );
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document.write( "The denominator is zero at x= 3;  so this value is excluded from the domain.\r\n" );
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document.write( "The numerator   is zero at x= 4  and x=-3;  so these values are excluded from the solution set.\r\n" );
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document.write( "After canceling the common factor (x+3) in the numerator and denominator, you get the function in the form  .\r\n" );
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document.write( "It is greater than 0, when linear binomials are EITHER both negative OR both positive. \r\n" );
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document.write( "So the solution set is the union of intervals  {x < -3} U (-3 < x < 2} U {x > 4},   or    (-oo,-3) U (-3,2) U (4,oo).      ANSWER>\r\n" );
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document.write( "See the plot below\r\n" );
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document.write( "    \r\n" );
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document.write( "    Plot y = \r\n" );
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document.write( "Notice that the point x = -3 is the  in the domain of the function: formally, the function IS NOT DEFINED at this point.\r\n" );
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