Final answer:
To add or subtract the fractions (3x+1)/(2x-5) and (x-7)/(2x-5), combine their numerators and keep the common denominator, simplifying to (2x+8)/(2x-5). The answer is checked for correctness, and the simplification process is confirmed to be reasonable.
Step-by-step explanation:
The student is asked to add or subtract the algebraic fractions (3x+1)/(2x-5)-(x-7)/(2x-5) and simplify the result. Since both fractions have the same denominator (2x-5), we can combine the numerators directly. The subtraction of the numerators yields (3x + 1) - (x - 7), which simplifies to 2x + 8. Therefore, the simplified form of the expression is (2x + 8)/(2x - 5).
To check if our answer is reasonable, we can verify that the original operation has been performed correctly and the resulting expression cannot be simplified further. The terms of the numerators are combined correctly, and the denominator remains the same because it does not have any common factors with the new numerator. Thus, our simplified expression is indeed reasonable.