Let

Putting

Which implies,

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

Now put x+2=0

Therefore, x=-2

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

B(-3)(-5)=-5

Now put x-3=0

Therefore, x=3

A(0)+B(0)+C(2)(5)=5

Now put x-1=0

Therefore, x=1

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

Now From equation (1) we get,