Absolute value laws - $|a \cdot b| = |a| \cdot |b|$ - Is my reasoning correct?

Question

I have the expression \begin{vmatrix}{ \dfrac{ (-1)\sqrt{n}(x+3) }{ \sqrt{n+1} } }\end{vmatrix}

We know that the absolute value laws state that $|a \cdot b| = |a| \cdot |b|$.

Therefore, would I be correct in saying that $ \begin{vmatrix}{ \dfrac{ (-1)\sqrt{n}(x+3) }{ \sqrt{n+1} } }\end{vmatrix} = \dfrac{ |x+3||-1|\sqrt{n}}{\sqrt{n+1} }$ ?

Thank you.

Answer 1

No. We have

$\begin{vmatrix}{ \dfrac{ (-1)\sqrt{n}(x+3) }{ \sqrt{n+1} } }\end{vmatrix}= \dfrac{ \sqrt{n}|(x+3)| }{ \sqrt{n+1} } $

Edit: You are right. My mistake, I have read $ \dfrac{ |x+3|-1\sqrt{n}}{\sqrt{n+1} }$