# For what x is #1 / ( x + 3 ) > 2/(x-3)#?

##### 1 Answer

#### Explanation:

Note that

Split the remaining possibilities into cases:

**Case**

In either case

#x-3 > 2x+6#

Subtract

#-9 > x#

Combining with the conditions of the case, that gives us the solution:

#x in (-oo, -9)#

**Case**

*and reverse the inequality* to get:

#x-3 < 2x+6#

Subtract

#-9 < x#

Combining with the conditions of the case, that gives us the solution:

#x in (-3, 3)#

**Conclusion**

Putting the two cases together, the original inequality holds for all

#x in (-oo, -9) uu (-3, 3)#