Final answer:
To divide (a²+10a+25)/(a+5) by (a²-25)/(a-5) and reduce to lowest terms, factor the numerator and denominator of both fractions, cancel out common factors, and simplify to (a+5)/(a-5).
Step-by-step explanation:
To divide (a²+10a+25)/(a+5) by (a²-25)/(a-5) and reduce to lowest terms, we can first factor the numerator and denominator of both fractions. The numerator of the first fraction can be factored as (a+5)(a+5), and the numerator of the second fraction can be factored as (a+5)(a-5). The denominator of the first fraction can be factored as (a+5) and the denominator of the second fraction can be factored as (a-5)(a+5).
Next, we can rewrite the expression as ((a+5)(a+5))/(a+5) - (a+5)(a-5)/(a-5)(a+5). Since (a+5) appears in both fractions, we can cancel it out, leaving us with (a+5) in the numerator of the first fraction and (a-5) in the numerator of the second fraction.
Therefore, the simplified expression is (a+5)/(a-5).
Learn more about Dividing Algebraic Fractions