Questions: (3t+3)/(t-6) * (t^2-t-30)

Solution Steps

To solve the given problem, we need to multiply the two expressions and simplify the result. The first step is to factorize both the numerator and the denominator where possible. Then, we can cancel out any common factors to simplify the expression.

1. Factorize the numerator and the denominator of the given fractions.
2. Multiply the fractions.
3. Simplify the resulting expression by canceling out common factors.

We start with the expression

\[ \frac{3t + 3}{t - 6} \cdot (t^2 - t - 30). \]

First, we factor the numerator \(3t + 3\) and the quadratic \(t^2 - t - 30\):

\[ 3t + 3 = 3(t + 1), \]

and

\[ t^2 - t - 30 = (t - 6)(t + 5). \]

Substituting the factored forms back into the expression, we have:

\[ \frac{3(t + 1)}{t - 6} \cdot (t - 6)(t + 5). \]

Next, we can cancel the common factor \((t - 6)\) from the numerator and the denominator:

\[ 3(t + 1)(t + 5). \]

The simplified expression is:

\[ 3(t + 1)(t + 5). \]

Final Answer