Let

Putting

Which implies,

A(x+1)(2x+3)+B(x-1)(2x+3)+C(x-1)(x+1)=2x-3

Now put x+1=0

Therefore, x=-1

A(0)+B(-1-1)(-2+3)+C(0)=-2-3

Now put x-1=0

Therefore, x=1

A(2)(2+3)+B(0)+C(0)=-1

Now put 2x+3=0

Therefore,

.Now From equation (1) we get,