How can I evaluate: $\lim_{x \to \infty} \sqrt{x^2 + 4x} - \sqrt{x^2 - 5x}$ I need to find this limit:
$$\lim_{x \to \infty} \sqrt{x^2 + 4x} - \sqrt{x^2 - 5x}$$
The answer I got from using the limit laws is $\sqrt{\infty} - \sqrt{\infty}$.
How do I proceed now?
Added I took the conjugate of the function and I got a new and probably better function to work with: $$\lim_{x\to \infty}\frac{9x}{\sqrt{x^2 + 4x} + \sqrt{x^2-5x}}$$

Multiply and divide by $$\sqrt{x^2+4x} +\sqrt{x^2-5x}$$
$$\lim_{x\to \infty} \frac{9x}{\sqrt{x^2+4x} +\sqrt{x^2-5x}}$$
$$\lim_{x\to \infty} \frac{9}{\frac{\sqrt{x^2+4x}}{x} +\frac{\sqrt{x^2-5x}}{x}}$$
