Final answer:
To simplify (rp-rq)/(3p-39), factor out common elements, resulting in (r(p-q))/(3(p-13)) which is the simplified form of the algebraic fraction.
Step-by-step explanation:
To simplify the algebraic fraction (rp-rq)/(3p-39), let's first look for common factors in the numerator and the denominator. Notice that both terms in the numerator have an r, and both terms of the denominator are divisible by 3.
Factoring out the common element r from the numerator gives us: r(p-q). Similarly, factoring out 3 from the denominator gives us: 3(p-13).
Now, our expression looks like this: (r(p-q))/(3(p-13)). There are no further common factors that can be cancelled out, so this is the simplified form of the fraction.