solve 4(x+2)^-1 - (3x)^-1 = 10(x+2)^-1

We'll rewrite it to make it easier to work with. In particular we move all like terms to the same side of the equation: 


 
which simplifies to... 

 

Now notice that this is a proportion, so we can cross multiply then divide: 
 
 

 
then x = -2/19 


:)