The solution of inequality (x+1)(x²+1)^1/2>x²-1 is

(a) {-1} U [2,infinite)

(b) [-1,infinite)

(c){-4}u[2,3]

(d)(-5,infinite)

(x+1)(x²+1)^1/2>x²-1

(x+1)(x²+1)^1/2>(x-1)(x+1)

either x=-1 or

case 1:x>-1

(x²+1)^1/2>x-1

squaring both side,

(x²+1)>x²+1 +2x

therefore x>0

case 2: x<-1

(x²+1)^1/2<x-1

therefore, x<0

therefore, answer is [-1,infinte)