YES anon understood what you wanted and gave you a correct answer!
I shall show you
$$\\\frac{2x-1}{x+2}=A+\frac{B}{x+2}\\\\
$multiply both sides by (x+2)$\\
2x-1=A(x+2)+B\\
2x-1=Ax+2A+B\\
2x-1=Ax+(2A+B)\\
$ equating co-efficients$\\
2=A\\
-1=2A+B\\
-1=4+B\\
B=-5\\
so\\
\frac{2x-1}{x+2}=2+\frac{-5}{x+2}\\\\$$
so maybe you owe anon an appology 