What is Rationalizing Infinite Limits: Useful Techniques to Simplify Limits
When a limit at infinity gives an indeterminate form like ∞ − ∞ with a square root, multiply by the conjugate to rationalize it. For example, √(x² + x) − x = x / (√(x² + x) + x), and dividing top and bottom by x shows the limit as x → ∞ is 1/2. […]