# Is the answer key wrong? or it's me? ok, so im reviewing for a math test and the following question

auto23652im 2022-07-02 Answered
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.
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## Answers (2)

Freddy Doyle
Answered 2022-07-03 Author has 20 answers
$\frac{\sqrt{2}}{\sqrt{x-3}}=\frac{\sqrt{2}\cdot \sqrt{x-3}}{\sqrt{x-3}\cdot \sqrt{x-3}}=\frac{\sqrt{2\cdot \left(x-3\right)}}{{\left(\sqrt{x-3}\right)}^{2}}=\frac{\sqrt{2x-6}}{x-3}$

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Desirae Washington
Answered 2022-07-04 Author has 5 answers
The answer key is right (it's you): You must have multiplied numerator by $\sqrt{x-3}$, not $\sqrt{x+3}$

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