32x+3−1(2x−3)=44x2−9

We are given: ${\displaystyle \frac{3}{2x+3}-1(2x-3)=\frac{4}{4x^2-9}}$
Factor $4x^2-9$: ${\displaystyle \frac{3}{2x+3}-1(2x-3)=\frac{4}{(2x+3)(2x-3)}}$
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: $x=4$