Final answer:
The expression (x²-25)/(x²+4x-5) is simplified by factoring the numerator as a difference of squares and the denominator into binomial factors, then cancelling the common terms to get (x-5) / (x-1).
Step-by-step explanation:
To simplify the expression (x2-25)/(x2+4x-5), we should factor both the numerator and the denominator, if possible.
First, notice that the numerator is a difference of squares, which factors into (x+5)(x-5).
Next, we factor the denominator. The denominator can be factored into its binomial factors of (x+5)(x-1), since (x+5)(x-1) = x2 + 4x - 5.
Now, we have:
((x+5)(x-5)) / ((x+5)(x-1))
We can cancel out the (x+5) terms, leading to:
(x-5) / (x-1)
This is the most simplified form of the expression as it cannot be further factored or simplified.