Final answer:
The correct answer is option B, which represents the difference between the expressions (2x + 5)/(x² - 3x) and (x + 1)/x² as (x + 1)/(x(x - 3)) after factorization and simplification.
Step-by-step explanation:
The difference in the expressions (2x + 5)/(x² - 3x) and (x + 1)/x² is found by combining them over a common denominator. In order to do this, we first factor the denominator of the first expression, which is x² - 3x, into x(x - 3).
We notice that the second expression already has the denominator x², which can also be written as x(x), implying a common term of x in both denominators
Next, we need to make the denominators the same, which can be achieved by multiplying the numerator and denominator of the second fraction by (x - 3), resulting in (x + 1)(x - 3) over x²(x - 3).
Now we can combine the fractions: ((2x + 5) - (x + 1)(x - 3)) over x(x - 3), which simplifies to ((2x + 5) - (x² - 2x - 3)) over x(x - 3).
Simplifying further, we cancel out common terms and combine like terms in the numerator to find our final expression, which gives us the correct answer: (x + 1)/(x(x - 3)). Therefore, option B is the correct answer.