Question 1040834
Multiply left and right by simplest common denominator.


{{{3x+4=A(x-1)(x+2)+B(x+2)+C(x-1)^2}}}


Simplify right side.


{{{3x+4=Ax^2-Ax-2A+Bx+2B+Cx^2-2Cx+C}}}


Form the right side into simplified decreasing powers of x.


{{{3x+4=(A+B)x^2(B-A-2C)x+(2B-A+C)}}}


Compare the corresponding parts or coefficients to write the system of equations.


{{{system(A+B=0,B-A-2C=3,2B-A+C=4)}}}
Finish!  Solve the system.