Final answer:
To simplify the expression (x²+10x+25)/(x²-25), factor the numerator to (x+5)² and the denominator to (x+5)(x-5), then cancel out the common factor to get (x+5)/(x-5). Remember that x cannot be -5 as it would make the original denominator zero.
Step-by-step explanation:
To simplify the rational expression (x²+10x+25)/(x²-25), we start by factoring both the numerator and the denominator. The numerator is a perfect square trinomial, so it factors into (x+5)². The denominator is a difference of squares and factors into (x+5)(x-5).
Now, the expression looks like this: ((x+5)²) / ((x+5)(x-5)). Notice that (x+5) appears in both the numerator and denominator, so we can cancel one (x+5) from both, leaving us with:
(x+5) / (x-5)
This is the simplified form of the original expression. However, keep in mind that when simplification involves cancelling out factors, the values that make those factors zero are not part of the domain. In this case, x cannot be -5 because it would make the original denominator zero, which is undefined in mathematics.