Answer: is option D: (r+5)(r-3)/(r-2)².
Step-by step explanation:
1. We start with the expression (r+5)/(r²+5r-14).
2. We factorize the denominator r²+5r-14 as (r+7)(r-2).
3. Next, we look at the denominator r²+4r-21 and factorize it as (r+7)(r-3).
4. Now, we can rewrite the expression as (r+5)/[(r+7)(r-2)] divided by [(r+7)(r-3)].
5. To divide by a fraction, we can multiply by its reciprocal. So, we multiply by the reciprocal of [(r+7)(r-3)], which is 1/[(r+7)(r-3)].
6. Multiplying the numerators and denominators, we get (r+5)(r-3)/[(r+7)(r-2)] * 1/[(r+7)(r-3)].
7. Simplifying further, we can cancel out the (r-3) terms in the numerator and denominator, leaving us with (r+5)/(r-2).
8. And that's the final answer!
