document.write( "Question 1148151: I have to solve the rational inequality and write the answer in interval notation. Could you please provide step by step guidance. I can solve, just want to make sure I have the correct steps.\r
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Algebra.Com's Answer #769506 by ikleyn(52784) $\"\"$ $\"About$

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document.write( "In your rational function, the numerator is equal to  (x-4)*(x+3),\r\n" );
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document.write( "while the denominator is  (x-2)*(x+3).\r\n" );
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document.write( "Therefore, this rational function is equal to\r\n" );
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document.write( "      > 0         (1)\r\n" );
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document.write( "everywhere, where the last rational function is defined, except x= -3, where the original rational function is not defined, at all.\r\n" );
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document.write( "Thus our task is to find the solutions of the inequality (1) everywhere, except x= -3.\r\n" );
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document.write( "The function (1) has two critical points  x= 4 and x= 2, where the numerator and denominator change their signs.\r\n" );
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document.write( "In the interval  x < 2, both the numerator and denominator of the function (1) are negative;  so the function (1) is positive.\r\n" );
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document.write( "In the interval 2 < x < 4, the numerator of (1) is negative, while the denominator is positive, so the function (1) is negative.\r\n" );
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document.write( "In the interval x > 4,  both the numerator and denominator of (1) are positive, so the function (1) is positive.\r\n" );
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document.write( "Now I am ready to present the \r\n" );
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document.write( "ANSWER :  The original function is positive in the intervals \r\n" );
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document.write( "                 (,), (-3,2), and (,).\r\n" );
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