Answer
$\frac{(t-5)(3t+1)(2t+11)}{(3t)(2t-55)(t+1)}$
Work Step by Step
In factored form, the given is equivalent to
$$
\frac{6t(t-5)}{(2t-55)(t+1)}\cdot\frac{(3t+1)(2t+11)}{6t(3t)}
.$$
Cancelling factors that are common to both the numerator and the denominator, the expression above is equivalent to
$$\begin{aligned}
&
\frac{\color{red}{6t}\color{black}(t-5)}{(2t-55)(t+1)}\cdot\frac{(3t+1)(2t+11)}{\color{red}{6t}\color{black}(3t)}
\\&=
\frac{(t-5)(3t+1)(2t+11)}{(3t)(2t-55)(t+1)}
.\end{aligned}$$Hence, the given expression simplifies to $\frac{(t-5)(3t+1)(2t+11)}{(3t)(2t-55)(t+1)}$.
