the ans is 1.
after multiplying with ax in denominator we get
{6a[(rootx^2+ax+a^2)] - root(x^2+a^2)}/{6ax+2a^2-1/x-xe^1/x}
=take x common fm num. and denom.
=x^2{6a[root(1+a/x+(a/x)^2)]-root(1+(a/x)^2)/x^2{6a+2a^2/x-1/x^2-e^1/x}
=6a-1/6a-1=1(on applying x tends to infinity)