Quantity A:
1 / (1 - 1/( 1 + 1/x))
= 1 / (1 - x/( x + 1))
= (x + 1) / (x + 1 - x)
= x + 1

could you explain the bold? How did you reach (x + 1) / (x + 1 - x)

See the steps in attached image file.

We can also use comparison.

1) Set a = x/2 for simplicity in writing.
2) We can cross multiply because x>0, so A = 1 + 1 / (1-a) and B = 1 - 1/(1+a)
3) Subtract 1 from both sides to get A = 1 / (1-a) and B = -1/(1+a)
4) Cross multiply again to get A = 1 / (1-a) and B = 1 / (1+a)
5) Cross multiply again to get A = 1+a and B = 1 - a
6) Subtract both sides by 1 and substitute a = x/2 to get A = 1/x and B = -1/x
7) Since x >= 2, A will always be greater than B

--> Answer is A

by simplifying both the quantities

quan A: x+1
quan B: (x-1)/(2x-1)

for x=2
quan A =3
quan B =(1/3)=.333
quan A > quan B

for x=2.1
quan A =3.1
quan B =(1.1/3.2)=.34375
quan A > quan B

so the answer is A

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