To simplify this expression, we first need to find a common denominator for the fractions involved.

The expression is:

(3/2 + 3/t) / (t/t + 6 - 1/t)

To find a common denominator for the fractions, we first need to simplify the second fraction, t/t. This simplifies to 1. Therefore, the expression becomes:

(3/2 + 3/t) / (1 + 6 - 1/t)

Now, simplify the terms in the second fraction:

(3/2 + 3/t) / (7 - 1/t)

Next, find a common denominator for the fractions in the numerator:

Numerator: (3t + 6) / 2t

Substitute this back into the expression:

(3t + 6) / 2t / (7 - 1/t)

Now, to divide by a fraction, we can multiply by its reciprocal:

(3t + 6) / 2t * t / (7t - 1)

Multiplying the numerators and denominators, we get:

(3t^2 + 6t) / (2t * 7t - 2t)

Simplify this expression:

(3t^2 + 6t) / (14t^2 - 2t)

Therefore, the simplified expression is:

(3t^2 + 6t) / (14t^2 - 2t)