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: $$\lim_{x\to \infty}\frac{9x}{\sqrt{x^2 + 4x} + \sqrt{x^2-5x}}$$

$$\lim_{x \to \infty} \sqrt{(x^2)+4x} - \sqrt{(x^2)-5x}$$
$$\lim_{x \to \infty} {(x^2)+4x - (x^2)+5x\over\sqrt{(x^2)+4x} +\sqrt{(x^2)-5x}}$$
$$\lim_{x \to \infty} {9x\over\sqrt{(x^2)+4x} +\sqrt{(x^2)-5x}}$$
$$\lim_{x \to \infty} {9\over\sqrt{(x^2)/x^2+4x/x^2} +\sqrt{(x^2)/x^2-5x/x^2}}$$
$$\lim_{x \to \infty} {9\over\sqrt{1+4/x} +\sqrt{1-5/x}}$$
$${9\over\sqrt{1} +\sqrt{1}}={9\over 2}$$
