Simplify
(a) `sqrt(9-6a+a^(2))+sqrt(9+6a+a^(2))` if `a lt -3`.
`(b) (1)/(sqrt([x+2sqrt((x-1))]))+(1)/(sqrt([x-2sqrt((x-1))]))` If `1 lt x lt 2`.

Answer

Let's solve the given problems step by step.

### Part (a): Simplify \( \sqrt{9 - 6a + a^2} + \sqrt{9 + 6a + a^2} \) if \( a < -3 \).

1. **Recognize the expressions under the square roots**:
\[ \sqrt{9 - 6a + a^2} = \sqrt{(a - 3)^2} \]
\[ \sqrt{9 + 6a + a^2} = \sqrt{(a + 3)^2} \]

2. **Apply the property of square roots**:
Since \( a < -3 \), both \( a - 3 \) and \( a + 3 \) are negative. Therefore:
\[ \sqrt{(a - 3)^2} = -(a - 3) = -a + 3 \]
\[ \sqrt{(a + 3)^2} = -(a + 3) = -a - 3 \]

3. **Combine the results**:
\[ \sqrt{9 - 6a + a^2} + \sqrt{9 + 6a + a^2} = (-a + 3) + (-a - 3) \]
\[ = -a + 3 - a - 3 = -2a \]

**Final Result for Part (a)**:
\[ \sqrt{9 - 6a + a^2} + \sqrt{9 + 6a + a^2} = -2a \]