Find all excluded values for the expression. That is, find all values of \( w \) for which the expression is undefined. \( \frac{w^{2}-w-20}{w^{2}-14 w+45} \) If there is more than one value, separate them with commas. \( w=\square \)

To find the excluded values for the expression \( \frac{w^{2}-w-20}{w^{2}-14w+45} \), we need to determine the values of \( w \) for which the expression is undefined. This occurs when the denominator of the fraction is equal to zero. Let's set the denominator equal to zero and solve for \( w \): \[ w^{2} - 14w + 45 = 0 \] Now, we can solve this quadratic equation to find the values of \( w \) for which the expression is undefined. Solve the quadratic equation by following steps: - step0: Solve by factoring: \(w^{2}-14w+45=0\) - step1: Factor the expression: \(\left(w-9\right)\left(w-5\right)=0\) - step2: Separate into possible cases: \(\begin{align}&w-9=0\\&w-5=0\end{align}\) - step3: Solve the equation: \(\begin{align}&w=9\\&w=5\end{align}\) - step4: Rewrite: \(w_{1}=5,w_{2}=9\) The excluded values for the expression \( \frac{w^{2}-w-20}{w^{2}-14w+45} \) are \( w = 5 \) and \( w = 9 \).