document.write( "Question 728270: solve the inequality and express the solution set in interval notation.
\n" ); document.write( "6/(x+4) > 6/(x-1) \n" ); document.write( "

Algebra.Com's Answer #445391 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"6%2F%28x%2B4%29+%3E+6%2F%28x-1%29\"$ , divide both sides by 6,
\n" ); document.write( " $\"1%2F%28x%2B4%29%3E1%2F%28x-1%29\"$
\n" ); document.write( " $\"1%2F%28x%2B4%29-1%2F%28x-1%29%3E0\"$
\n" ); document.write( " $\"%28%28x-1%29-%28x%2B4%29%29%2F%28%28x%2B4%29%28x-1%29%29%3E0\"$
\n" ); document.write( " $\"%28-5%29%2F%28%28x%2B4%29%28x-1%29%29%3E0\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "One of the binomials of the denominator must be positive while the other is negative. The critical points to test separating the intervals are at x=-4 and x=1. Pick any value for x in each of these three intervals and test:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(-infinity, -4)
\n" ); document.write( "(-4, +1)
\n" ); document.write( "(+1, infinity)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The numerator is negative. You must choose the intervals which make the entire denominator itself be negative. \n" ); document.write( "

\n" );