Sure, let's break down the given expression step-by-step:
We are given the expression [tex]\(\frac{1}{\sqrt{x-1}} + \sqrt{x-1}\)[/tex].
1. Identify the components:
- The first term is [tex]\(\frac{1}{\sqrt{x-1}}\)[/tex].
- The second term is [tex]\(\sqrt{x-1}\)[/tex].
2. Simplify the terms:
- The term [tex]\(\sqrt{x-1}\)[/tex] is already in its simplest form.
- The term [tex]\(\frac{1}{\sqrt{x-1}}\)[/tex] is also in its simplest form because you can't simplify it further without additional context or values.
3. Combine the simplified terms:
- Since both terms are already simplified, you simply combine them as given: [tex]\(\frac{1}{\sqrt{x-1}} + \sqrt{x-1}\)[/tex].
Thus, the given expression in its simplified form is:
[tex]\[ \frac{1}{\sqrt{x-1}} + \sqrt{x-1} \][/tex]
This is the final result of the expression.
