Question 503298
The goal is to eliminate the denominators.
You should first make sure you can not factor anything, and then proceed.
Find the common denominator (every number/polynomial in the denominator must be represented)
In this case our common denominator is (2x-3)(x+2)

Multiply each side by (2x-3)(x+2)

Since (7/x+2) already contains x+2, these cancel, and you only multiply 
7(2x-3)= 14x-21
Likewise with 4/2x-3. The 2x-3 on the denominator cancels and you multiply 4(x+2)= 4x+8

At this point your problem should look like this:
(14x-21)- (4x+8).
Since we have subtraction, we treat the negative sign like distributing a -1.
We then have:
14x-21-4x-8
Condense:
10x-29
Always check to see if you can further factor.
In this case, you can not. 
Answer=10x-29