How can find this limit? $\lim_{x\to-∞}(\sqrt{x^2+6x}-\sqrt{x^2-2x})$ $$\lim_{x\to-∞}(\sqrt{x^2+6x}-\sqrt{x^2-2x})$$
plugging in infinity gives infinity - infinity, what kind of manipulation can I do to solve this?

$$\sqrt{x^2+6x}=\sqrt{x^2+6x+9-9}=\sqrt{(x+3)^2-9}\approx |x|+3,\text{ as }x\to-\infty$$
$$\sqrt{x^2-2x}=\sqrt{x^2-2x+1-1}=\sqrt{(x-1)^2-1}\approx |x|-1,\text{ as }x\to-\infty$$
