document.write( "Question 1168423: For the function ​g(x)=x+8/x+2, solve the following inequality.
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Algebra.Com's Answer #793015 by ikleyn(53764)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "In order for  g(x)  be positive,  both the numerator and denominator should be EITHER both positive, OR both negative.\r\n" );
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document.write( "So, we consider two cases.\r\n" );
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document.write( "Case (a).  x+8 > 0  AND  x+2 > 0.\r\n" );
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document.write( "     The solution set to these two inequalities is  {x > - 8}  AND  {x > - 2}.\r\n" );
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document.write( "     The last two inequalities are EQUIVALENT to  one single inequality  x > -2.\r\n" );
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document.write( "Case (b).  x+8 < 0  AND  x+2 < 0.\r\n" );
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document.write( "     The solution set to these two inequalities is  {x < - 8}  AND  {x < - 2}.\r\n" );
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document.write( "     The last two inequalities are EQUIVALENT to  one single inequality  x < -8.\r\n" );
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document.write( "Thus the final solution to your problem is this:\r\n" );
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document.write( "    {x < -8}  or  {x > -2},\r\n" );
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document.write( "Or in the interval form\r\n" );
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document.write( "    (-oo,-8) U {-2,oo)    (union of two sets).\r\n" );
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