Find limit limx →∞ √ (x ^ 3 + x) - (√ x)

Find limit limx →∞ √ (x ^ 3 + x) - (√ x)

Limx → + ∞ (3 ^ x + 9 ^ x) ^ (1 / x)
It seems that we need to use the important limit

Limx →∞ (3 ^ x + 1) ^ (1 / x) = limx →∞ e ^ ln (3 ^ x + 1) ^ (1 / x) = e ^ limx →∞ ln (3 ^ x + 1) / x = e ^ limx →∞ 3 ^ x * Ln3 / (3 ^ x + 1) = e ^ limx →∞ Ln3 / (1 + 1 / 3 ^ x) = e ^ Ln3 = 3, the original formula = limx →∞ [(3 ^ x) * (3 ^ x + 1)] ^ (1 / x) = 3 * limx →∞ (3 ^ x + 1) ^ (1 / x) = 3 * 3 = 9

How much does 3x-2x equal to is the solution of equation x, not multiplication

3x/4-2x/3=1x/12
Read as one twelfth X