find the values of A,B and C such that
i see that it is repeated linear, but the x^2+4 is confusing me.
"repeated linear" -?? I've never heard of that. Multiply by the LCD to get
$\displaystyle 2x - 3 = A(x^2 + 4) + (Bx + C)(x + 1)$
$\displaystyle 2x - 3 = Ax^2 + 4A + Bx^2 + (B + C)x + C$
$\displaystyle 2x - 3 = (A + B)x^2 + (B + C)x + (4A + C)$
Now equate coefficients.