Sure, let's solve the expression step by step.
First, simplify the fraction in the numerator:
[tex]\[
\frac{-6 + 5}{9} = \frac{-1}{9}
\][/tex]
Next, we need to deal with the division by the fraction [tex]\(\frac{-1}{6}\)[/tex]. Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we need the reciprocal of [tex]\(\frac{-1}{6}\)[/tex]:
[tex]\[
\text{Reciprocal of } \frac{-1}{6} \text{ is } \frac{6}{-1} = -6
\][/tex]
Now, we can perform the division by multiplying [tex]\(\frac{-1}{9}\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
\frac{-1}{9} \times -6
\][/tex]
Perform the multiplication:
[tex]\[
\left(\frac{-1 \times -6}{9}\right) = \frac{6}{9} = \frac{2}{3}
\][/tex]
Thus, the result is:
[tex]\[
\frac{2}{3} \approx 0.6666\ldots
\][/tex]
So, the detailed breakdown of the solution gives the final result:
[tex]\[
\left(\frac{-6+5}{9}\right) \div \frac{(-1)}{6} = 0.6666666666666666
\][/tex]
