The solution set of the inequality is of form (a+b).

x/((1-x)^1/2 +x^1/2 )-x/((1-x)^1/2-x ^1/2)>2/x^1/2

The value of a+b=

(a)14

(b)infinite

(c)3/2

(d)11/4

x/((1-x)^1/2 +x^1/2 )-x/((1-x)^1/2-x ^1/2)>2/x^1/2

x^3/2[((1-x)^1/2 -x^1/2 ) - ((1-x)^1/2 +x^1/2 )]>2[((1-x) -x )]

-2x² > 2(1-2x)

x² -2x+1>0

(x-1)²>0

always true,

thus infinite is the answer