We are given: $\frac{3}{2x+3}-1(2x-3)=\frac{4}{4{x}^{2}-9}$
Factor $4{x}^{2}-9$: $\frac{3}{2x+3}-1(2x-3)=\frac{4}{(2x+3)(2x-3)}$
We note that $x=\pm 3/2$ are excluded values based on the denominators.
Multiply both sides by the LCD which is $(2x+3)(2x-3)3(2x-3)-(2x+3)=4$ $6x-9-2x-3=4$ $4x-12=4$
Add 12 to both sides: $4x=16$
Divide both sides by 4: $x=4$