Simplify the expression and state the restrictions on the variable. \( \frac{9-u^{2}}{2 u^{2}-6 u} \) Part: \( \mathbf{0} / \mathbf{2} \) Part 1 of 2 Simplify. \[ \frac{9-u^{2}}{2 u^{2}-6 u}= \]

To simplify the expression \( \frac{9-u^{2}}{2 u^{2}-6 u} \), we first factor both the numerator and denominator. The numerator \( 9 - u^2 \) can be rewritten as \( (3 - u)(3 + u) \) using the difference of squares. The denominator \( 2u^2 - 6u \) can be factored by taking out a common factor of \( 2u \), giving us \( 2u(u - 3) \). So, the expression simplifies to: \[ \frac{(3 - u)(3 + u)}{2u(u - 3)} \] Next, we can cancel the common factor \( (3 - u) \) in the numerator and \( (u - 3) \) in the denominator (noting that \( (3 - u) = -(u - 3) \)): \[ = -\frac{(3 + u)}{2u} \] Thus, the simplified expression is: \[ -\frac{3 + u}{2u} \] Now, let's state the restrictions. The original denominator \( 2u^2 - 6u = 2u(u - 3) \) cannot equal zero. Thus, the restrictions on \( u \) are: \( u \neq 0 \) and \( u \neq 3 \).