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\frac{\left(t+1\right)\times 3}{9\left(-t-1\right)}
Divide \frac{t+1}{9} by \frac{-t-1}{3} by multiplying \frac{t+1}{9} by the reciprocal of \frac{-t-1}{3}.
\frac{t+1}{3\left(-t-1\right)}
Cancel out 3 in both numerator and denominator.
\frac{-\left(-t-1\right)}{3\left(-t-1\right)}
Extract the negative sign in t+1.
\frac{-1}{3}
Cancel out -t-1 in both numerator and denominator.
-\frac{1}{3}
Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.