If 0 < a < b then, for all x > 0, $$\frac{a + x}{b + x}$$ > 

Let assume any value for a,b and x that satisfy the above conditions.

Let say, a=1 and b=2 and x=5.

Then (a/b)=(1/2)=0.5.

and (a+x)/(b+x)=6/7=0.85.

So,(a+x)/(b+x) >(a/b).

but it is not greater than x or (b/a).

now,(1/x)=1/5=0.2

So,in this case (a+x)/(b+x)>(1/x).

But if we consider x=0.5 :

(a+x)/(b+x)=1.5/2.5=0.6.

but (1/x)=10/5=2.

So, in this case (a+x)/(b+x) is lesser than (1/x).

So, only option C is correct.