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Question Number 120843 by bramlexs22 last updated on 03/Nov/20

$$\underset{x\to 3}{\lim }\frac{\sqrt{\mathrm{x}+9-6\sqrt{\mathrm{x}}}}{\sqrt{\mathrm{x}}-3}?$$

Commented by Dwaipayan Shikari last updated on 03/Nov/20

$$\frac{\sqrt{12-6\sqrt{3}}}{\sqrt{3}-3}=-1$$

Answered by Jamshidbek2311 last updated on 03/Nov/20

$$\frac{\sqrt{3+9-6\sqrt{3}}}{\sqrt{3}-3}=\frac{\sqrt{3(4-2\sqrt{3})}}{\sqrt{3}-3}=\frac{\sqrt{3{(\sqrt{3}-1)}^2}}{\sqrt{3}-3}=$$$$\frac{(\sqrt{3}-1)\sqrt{3}}{\sqrt{3}-3}=\frac{3-\sqrt{3}}{\sqrt{3}-3}=-1$$

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