differentiating partial fraction

i have been given a function to be expressed in partial fractions then differentiate it.

$\displaystyle \frac{4x^2+3x-2}

{(u+1)(2u+3)}$

am stuck at the point where i cant eliminate one of the variables.

using $\displaystyle \frac{4x^2+3x-2}

{(u+1)(2u+3)}$

$\displaystyle 4x^2+3x-2 ={A}/(u+1)+{B}/(2u+3) $

$\displaystyle 4x^2+3x-2 = A(2U+3)+B(U+1)$

eliminating B by letting U = -1

therefore A =-1 (assuming i did it correctly)

i cant seem to eliminate A to get a value for B. am i doing something wrong.