Question

Perform the indicated operation: (r^2 / (r - s)) - (s^2 / (r - s)) =

A) -r - s
B) 1
C) (r + s) / (r - s)
D) r + s

Answer 1

The indicated operation (r^2 / (r - s)) - (s^2 / (r - s)) simplifies to r + s after factoring the numerator as a difference of squares and canceling out the common terms.

Step-by-step explanation:

To perform the indicated operation (r^2 / (r - s)) - (s^2 / (r - s)), notice that both terms have the same denominator. This allows us to combine the numerators over a common denominator directly.

Thus, we have:

(r^2 - s^2) / (r - s)

We recognize that r^2 - s^2 is a difference of squares, which factors as (r + s)(r - s). So the expression simplifies to:

(r + s)(r - s) / (r - s)

The (r - s) terms cancel out, leaving us with the final answer:

r + s