Final answer:
Dividing common terms and factors, resulting in the simplified form (2/3)(x - 3)^2(x + 1).
Step-by-step explanation:
To simplify the given rational expression 4x( x - 3 )3 ( x +1) / 6x2 ( x - 3), we need to factor and reduce common terms.
The expression can be simplified step-by-step as follows:
- First, we can cancel a x from the numerator and denominator.
- Next, we can reduce the (x - 3) term since it appears raised to a power in the numerator and once in the denominator, which leaves us with (x - 3)2 in the numerator.
- Then we simplify the coefficients 4 and 6 by dividing both by their greatest common divisor, which is 2.
After performing these simplifications, the final expression is (2/3)(x - 3)2(x + 1).