Sure, let's break down the given expression step by step and simplify it where possible.
Given expression:
[tex]\[
\frac{\sqrt{2n} - \sqrt{3 - n^2}}{n - 1}
\][/tex]
Step 1: Identify components of the expression
The numerator of the fraction is [tex]\(\sqrt{2n} - \sqrt{3 - n^2}\)[/tex].
The denominator of the fraction is [tex]\(n - 1\)[/tex].
Step 2: Analyze the expression for simplification
To simplify the expression, let's examine if the terms in the numerator or denominator can be simplified individually.
However, in this case, there do not seem to be any common factors or identities that apply directly to simplify this further by just algebraic manipulation without additional context (like limits or specific values for [tex]\(n\)[/tex]).
Step 3: Final simplified form
The original expression already represents a simplified form. The expression [tex]\(\frac{\sqrt{2n} - \sqrt{3 - n^2}}{n - 1}\)[/tex] does not lend itself to obvious algebraic simplifications beyond this form without additional contexts such as limits or specific values of [tex]\(n\)[/tex].
Therefore, the simplified expression remains:
[tex]\[
\frac{\sqrt{2n} - \sqrt{3 - n^2}}{n - 1}
\][/tex]
This is the simplified form of the given expression, and no further simplification is possible given the current context.
