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:
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)