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\frac{3\left(-2\right)+1}{-2\times 3}
Express \frac{\frac{3\left(-2\right)+1}{-2}}{3} as a single fraction.
\frac{-6+1}{-2\times 3}
Multiply 3 and -2 to get -6.
\frac{-5}{-2\times 3}
Add -6 and 1 to get -5.
\frac{-5}{-6}
Multiply -2 and 3 to get -6.
\frac{5}{6}
Fraction \frac{-5}{-6} can be simplified to \frac{5}{6} by removing the negative sign from both the numerator and the denominator.