<s>[INST] Rationalizing the denominator of $\frac{\sqrt {2}}{\sqrt {x-3}}$ ok, so im reviewing for a math test and the following question is from the practice final exam.

Rationalize the denominator in the example:
$$\frac{\sqrt {2}}{\sqrt {x-3}}$$

After multiplying both the numeration and denominator by the conjugate of the denominator, I got $$\frac{\sqrt {2x+6}}{x-3}$$
But, in the answer key the answer is  $$\frac{\sqrt {2x-6}}{x-3}$$
The problem looks quite simple, but I'm not sure what is the answer.
 [/INST] $$\frac{\sqrt{2}}{\sqrt{x-3}}=\frac{\sqrt{2}\cdot\sqrt{x-3}}{\sqrt{x-3}\cdot\sqrt{x-3}}=\frac{\sqrt{2\cdot(x-3)}}{\left(\sqrt{x-3}\right)^2}=\frac{\sqrt{2x-6}}{x-3}$$
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