How do you find the following limit as x approaches infinity? $\lim_{x\to \infty} \sqrt{x^2+9} - \sqrt{x^2-2}$
I have tried multiplying by the conjugate but the square roots are throwing me off and I'm not sure what to do next. How do you solve this?

$$\sqrt{x^2+9}-\sqrt{x^2-2}=\frac{(\sqrt{x^2+9}-\sqrt{x^2-2})(\sqrt{x^2+9}+\sqrt{x^2-2})}{\sqrt{x^2+9}+\sqrt{x^2-2}}=\frac{x^2+9-x^2+2}{\sqrt{x^2+9}+\sqrt{x^2-2}}=\frac{11}{\sqrt{x^2+9}+\sqrt{x^2-2}}$$
$$\lim_{x \to \infty} \sqrt{x^2+9}-\sqrt{x^2-2}=\lim_{x \to \infty } \frac{11}{\sqrt{x^2+9}+\sqrt{x^2-2}}=0$$
