### Instruction: Find \[\dfrac{3}{\,\,\frac{6}{11}\,\,}.\].### Response: I notice that this is a fraction divided by another fraction, and I remember that I can simplify this by multiplying by the reciprocal of the denominator.
That is, I can rewrite this as \[\dfrac{3}{\,\,\frac{6}{11}\,\,}=\dfrac{3}{1}\times\dfrac{11}{6}.\]
I can also simplify this by canceling out any common factors between the numerator and the denominator.
I see that both 3 and 6 are divisible by 3, so I can divide them by 3 and get \[\dfrac{3}{1}\times\dfrac{11}{6}=\dfrac{1}{1}\times\dfrac{11}{2}.\]
Now I have a simple fraction that I can evaluate by dividing the numerator by the denominator.