Final answer:
To simplify the given expression, divide each term of the numerator by the term of the denominator and subtract the exponents.
Step-by-step explanation:
Simplifying expressions involves reducing them to their most concise form by combining like terms, performing operations, and applying various algebraic rules.
To simplify the given expression, we need to divide each term of the numerator by the term of the denominator and subtract the exponents. So,
(3x³-3x²+7x-7)/(27x⁴-147) = (3x³)/(27x⁴) + (-3x²)/(27x⁴) + (7x)/(27x⁴) + (-7)/(27x⁴) = 1/9x + -1/9x² + 7/27x³ + -7/27x⁴.