Final answer:
To simplify the algebraic expression 4x( x - 3 )³ ( x +1) / 6x² ( x - 3), we cancel out common terms and reduce the coefficients, resulting in the simplified form (x + 1)(x - 3)² / 3x.
Step-by-step explanation:
The given expression is 4x( x - 3 )³ ( x +1) / 6x² ( x - 3). To simplify the expression, we need to factor out common terms and reduce the expression:
- We first notice that the term (x - 3) is common in both numerator and denominator.
- We have x - 3 raised to the power of three in the numerator and just x - 3 once in the denominator, so we can cancel out one (x - 3) term, leaving us with (x - 3)² in the numerator.
- Additionally, there is an x in the numerator and x² in the denominator, which means we can divide out one x from both, leaving us with just x in the denominator.
- Finally, we can simplify the coefficients 4 and 6 by dividing both by 2, which gives us 2 in the numerator and 3 in the denominator.
The simplified expression is (x + 1)(x - 3)² / 3x.