Final answer:
More context is needed to determine what to multiply the numerator and denominator of the fraction (3x+1)/(x-5) by, as it depends on the goal of the operation.
Step-by-step explanation:
The student is asking about the process of multiplying a fraction by another quantity to simplify or change its form. Specifically, the question is what to multiply both the numerator and denominator of the fraction (3x+1)/(x-5) by. When simplifying a fraction or modifying it for a particular purpose, such as canceling units or comparing with another fraction, we may multiply the numerator and the denominator by the same quantity to keep the value of the fraction unchanged (since any number divided by itself is equal to 1). For example, if we need to clear a denominator in an equation, we might multiply by the reciprocal of the denominator. However, without a specific operation to perform or goal to achieve, there is no single answer to what the numerator and denominator should be multiplied by. More context is needed to give a precise operation.