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\frac{-8}{9\left(-4\right)}
Express \frac{-\frac{8}{9}}{-4} as a single fraction.
\frac{-8}{-36}
Multiply 9 and -4 to get -36.
\frac{2}{9}
Reduce the fraction \frac{-8}{-36} to lowest terms by extracting and canceling out -4.