$\frac{x}{(x+2)(x-2)}+\frac{4}{x-2}=\frac{3}{x+2}$

Step 1 ：Given the equation \(\frac{x}{(x+2)(x-2)}+\frac{4}{x-2}=\frac{3}{x+2}\)

Step 2 ：First, we eliminate the fractions by multiplying each term by the common denominator, which is \((x+2)(x-2)\)

Step 3 ：After simplifying, we get the equation \(\frac{3}{x + 2} = \frac{5x + 8}{x^2 - 4}\)

Step 4 ：Solving this equation, we find that the solution is \(x = -7\)

Step 5 ：This means that when \(x = -7\), the equation holds true

Step 6 ：Final Answer: The solution to the equation is \(\boxed{-7}\)