\(\dfrac{1}{x+2}+\dfrac{2}{2-x}=\dfrac{2x-3}{x^2-4}\)

\(\left(-\right)\dfrac{x-2}{\left(x+2\right)\left(x-2\right)}-\dfrac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{2x-3}{x^2-4}\)

\(\left(-\right)\dfrac{x-2}{x^2-4}-\dfrac{2x+4}{x^2-4}-\dfrac{2x-3}{x^2-4}=0\)

\(\left(-\right)x-2-2x-4-2x+3=0\)

\(\left(-\right)-3x-3=0\)

\(\left(-\right)-3x=3\)

\(\left(-\right)x=-1\)