Question 1172392
<pre>
{{{1/(x - 2) < 1/(x + 3)}}}

{{{1/(x - 2) - 1/(x + 3) < 0}}}

{{{((x + 3)-(x - 2))/((x - 2)(x + 3))<0}}}

{{{(x + 3-x + 2)/((x - 2)(x + 3))<0}}}

{{{(5)/((x - 2)(x + 3))<0}}}

Since the numerator is positive, the denominator must be negative.

{{{(x - 2)(x + 3)<0}}}

The critical numbers and 2 and -3

test region   test value    (+ or -)?    < 0?  
 x < -3           -4            +          no
-3 < x < 2         0            -         yes
   x > 2           3            +          no

So the solution is -3 < x < 2 

Interval notation (-3, 2)

Edwin</pre>