The problem presented in the image involves simplifying and evaluating a mathematical expression $Q$. The given expression is:

$Q = \left(\frac{1}{\sqrt{x-1}} - \frac{1}{\sqrt{x+1}}\right)\left(\frac{1}{\sqrt{x+1}} + \frac{2}{\sqrt{x-1}}\right)$

Part (a): Simplify the Expression $Q$

To simplify $Q$, let's expand the expression by multiplying the two terms together:

$Q = \left(\frac{1}{\sqrt{x-1}} - \frac{1}{\sqrt{x+1}}\right)\left(\frac{1}{\sqrt{x+1}} + \frac{2}{\sqrt{x-1}}\right)$

This can be expanded using the distributive property:

$Q = \frac{1}{\sqrt{x-1}} \cdot \frac{1}{\sqrt{x+1}} + \frac{1}{\sqrt{x-1}} \cdot \frac{2}{\sqrt{x-1}} - \frac{1}{\sqrt{x+1}} \cdot \frac{1}{\sqrt{x+1}} - \frac{1}{\sqrt{x+1}} \cdot \frac{2}{\sqrt{x-1}}$

Simplifying each term:

1. $\frac{1}{\sqrt{x-1}} \cdot \frac{1}{\sqrt{x+1}} = \frac{1}{\sqrt{(x-1)(x+1)}} = \frac{1}{\sqrt{x^2-1}}$
2. $\frac{1}{\sqrt{x-1}} \cdot \frac{2}{\sqrt{x-1}} = \frac{2}{x-1}$
3. $\frac{1}{\sqrt{x+1}} \cdot \frac{1}{\sqrt{x+1}} = \frac{1}{x+1}$
4. (\frac{1