To determine the excluded values for the expression [tex]\(-\frac{5}{6 - 9w}\)[/tex], we need to find the values of [tex]\(w\)[/tex] that make the denominator zero.
Here’s the step-by-step process:
1. Identify the denominator of the expression. The denominator is [tex]\(6 - 9w\)[/tex].
2. Set the denominator equal to zero since the expression is undefined when the denominator is zero:
[tex]\[
6 - 9w = 0
\][/tex]
3. Solve the equation for [tex]\(w\)[/tex]:
\begin{align}
6 - 9w &= 0 \\
-9w &= -6 \\
w &= \frac{-6}{-9} \\
w &= \frac{6}{9} \\
w &= \frac{2}{3}
\end{align}
Therefore, the value of [tex]\(w\)[/tex] that makes the expression [tex]\(-\frac{5}{6 - 9w}\)[/tex] undefined is [tex]\(w = \frac{2}{3}\)[/tex].
### Conclusion
[tex]\[
\boxed{\frac{2}{3}}
\][/tex]
This is the singular value for [tex]\(w\)[/tex] that causes the expression to be undefined. If you plug [tex]\(w = \frac{2}{3}\)[/tex] into the original expression, you will find that the denominator becomes zero, which confirms the expression is indeed undefined at this value.
