\(A=\dfrac{x}{x-2}-\dfrac{x^2+x-2}{x^2-4}=\dfrac{x^2+2x-x^2-x+2}{\left(x-2\right)\left(x+2\right)}=\dfrac{x+2}{\left(x-2\right)\left(x+2\right)}=\dfrac{1}{x-2}\)
\(A=\dfrac{x}{x-2}+\dfrac{x^2+x-2}{4-x^2}\left(x\ne\pm2\right).\)
\(A=\dfrac{x}{x-2}-\dfrac{\left(x-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{x}{x-2}-\dfrac{x-1}{x-2}=\dfrac{x-x+1}{x-2}=\dfrac{1}{x-2.}\)
A= \(\dfrac{x}{x-2}+\dfrac{x^2+x-2}{4-x^2}=\dfrac{-x\left(2+x\right)}{\left(2-x\right)\left(2+x\right)}+\dfrac{x^2+x-2}{\left(2-x\right)\left(2+x\right)}=\dfrac{-2x-x^2+x^2+x-2}{\left(2-x\right)\left(2+x\right)}=\dfrac{-x-2}{\left(2-x\right)\left(2-x\right)}=\dfrac{-1\left(x+2\right)}{\left(2-x\right)\left(2+x\right)}=\dfrac{-1}{2-x}\)