Decompose rational expressions into partial fractions
Find every coefficient in the stated real partial-fraction decomposition. Zero and fractional coefficients are allowed
\[\frac{-\frac{1}{2}x-1}{(2x+3)(x+1)}=\frac{A}{2x+3}+\frac{B}{x+1}\]
\[x\ne -\frac{3}{2},-1\]