Final answer:
To perform the operation and express the answer as a single fraction in simplest form, subtract the fractions (3/4) and (1/2x³) by finding a common denominator. The answer is ((3x³ - 2)/(4x³)).
Step-by-step explanation:
To perform the operation and express the answer as a single fraction in simplest form, we need to subtract the fractions (3/4) and (1/2x³). Since the fractions have different denominators, we need to find a common denominator. The least common multiple of 4 and 2x³ is 4x³. Multiplying the numerator and denominator of (3/4) by x³, we get (3x³/4x³). Now, subtracting (1/2x³) from (3x³/4x³) gives us ((3x³ - 2)/(4x³)). This is our answer, expressed as a single fraction in simplest form.