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.

$$\frac{\sqrt{2}}{\sqrt{x-3}}=\frac{\sqrt{2}\cdot\sqrt{x-3}}{\sqrt{x-3}\cdot\sqrt{x-3}}=\frac{\sqrt{2\cdot(x-3)}}{\left(\sqrt{x-3}\right)^2}=\frac{\sqrt{2x-6}}{x-3}$$