Lim [[√ (x + 2) (x + 1)] - x] x approaches infinity. How to calculate this problem? The answer is 1 / 2

Lim [[√ (x + 2) (x + 1)] - x] x approaches infinity. How to calculate this problem? The answer is 1 / 2

If it's true, it's 2 / 3lim [[(x + 2) (x + 1)] - x] = Lim [[[(x + 2) (x + 1)] - x] * [[(x + 2) (x + 1)] + x] / [(x + 2) (x + 1)] + x] = Lim [(x + 2) (x + 1) - x ^ 2] / [[(x + 2) (x + 1)] + x] = LIM (3x + 2) / [[(x + 2) (x + 1)] + x] (then the numerator denominator is divided by X at the same time