Fine the derivative of (2-1/x))/(x+3)

(2-1/x))/(x+3)  ....we could use the quotient rule here, but I always tend to forget it, so I prefer to write the denominator as a ( -1 ) power and just use  the product / chain rules....so we have

 y = (2 - x^-1) (x + 3)^-1

y ' =  x^-2(x + 3)^-1 - (2 - x^-1)(x +3)^-2

Which we could simplify as  (x+ 3)^-2 [ x^-2 (x + 3) - 2 + x^-1 ] = (x+ 3)^-2 [ 2x^-1 + 3x^-2 - 2 ]

[Note....there are several other acceptable forms ]

y =  (2 - x^-1) / (x + 3)

Using the quotient formula:

y'  =  [ (x + 3)(x^-2) - (2 - x^-1)(1) ] / (x + 3)²

y'  =  [ x^-1 + 3x^-2 - 2 + x^-1 ] / (x + 3)²

y'  =  ( 2x^-1 + 3x^-2 - 2 ) / (x + 3)²