√(x^2 + x - 1) - √(x^2 + 5)
= (√(x^2 + x - 1) - √(x^2 + 5))·(√(x^2 + x - 1) + √(x^2 + 5))/(√(x^2 + x - 1) + √(x^2 + 5))
= ((x^2 + x - 1) - (x^2 + 5))/(√(x^2 + x - 1) + √(x^2 + 5))
= (x - 6)/(√(x^2 + x - 1) + √(x^2 + 5))
= (1 - 6/x)/(√(1 + 1/x - 1/x^2) + √(1 + 5/x^2))
= 1/2