Final answer:
The expression (x-1)/(3x^2) simplifies to 1/3x - 1/x^2 when distributing the denominator to both parts of the numerator and simplifying each term.
Step-by-step explanation:
To simplify the expression (x-1)/(3x2) using quotient rule, we must realize that the quotient rule relates to differentiating functions in calculus, but here we seem to be looking for simplifying a rational expression by separating it into parts. A quotient of two terms can be split into the sum or difference of two separate fractions if they have common factors.
In this case, we can split the numerator and distribute the denominator to both parts:
(x/3x2) - (1/3x2)
Now, simplify each term:
- The x in the numerator and one x in the denominator of the first term cancel out, leaving us with 1/3x.
- The second term remains as is because there is nothing to cancel.
Thus, the simplified expression is 1/3x - 1/3x2 or B. 1/3x - 1/x2, if we recognize that 1/x2 is the same as 1/3x2.