Determine the value for A and B

Question

Determine the value for A and B such that A / x+1 + B / 3x+2 simplifies to 2x-1 / (x+1)(3x+2)

Answer 1

A/(x+1) + B/(3x+2) = (3x+2)A/(x+1)(3x+2) +(x+1)B/(3x+2)(x+1)

= (3xA +2A + Bx +B)/(3x+2)(x+1)

= [(3xA +Bx) +(2A+B)]/(3x+2)(x+1)

3A +B = 2

2A +B =-1

A = 3

B =-1-2A = -7

A=3, B =--7