Is the answer key wrong? or it's me?

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.

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.