To tackle the given mathematical problems, let's break down the equations step by step.

### Câu 5: Rút gọn \( Q \)

**a)** The expression for \( Q \) is:
\[
Q = \frac{\sqrt{b-1}}{\sqrt{b+1}} \cdot \frac{b-1}{b+1}
\]
We can simplify \( Q \) by recognizing that the two fractions can be combined:
\[
Q = \frac{(b-1)\sqrt{b-1}}{(b+1)\sqrt{b+1}}
\]

**b)** For \( b = 6 + 275 = 281 \):
Substituting this value into the expression:
\[
Q = \frac{(281-1)\sqrt{281-1}}{(281+1)\sqrt{281+1}} = \frac{280\sqrt{280}}{282\sqrt{282}}
\]

### Câu 6: Rút gọn \( A \)

**a)** The expression for \( A \) is:
\[
A = \frac{\sqrt{x}-1}{x^2-x} \cdot \left( \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x+1}} \right)
\]
First, manipulate the \( x^2-x \):
\[
x^2 - x = x(x-1)
\]
Now, simplify \( A \):
\[
A = \frac{\sqrt{x}-1}{x(x-1)} \cdot \left( \frac{2(\sqrt{x+1}-\sqrt{x})}{\sqrt{x(x+1)}} \right)
\]

**b)** For \( x = 4 + 2\sqrt{3} \):
Substituting into \( A \) will require calculating the individual terms, substituting back and simplifying accordingly.

### Câu 7: Tìm \( a \)

You can solve this by following a similar approach once you identify the specific expression for \( A \).

If you need further assistance with the calculations or specific methods for simplifications, please let me know!