Final answer:
To simplify the given rational function, factor the numerator and denominator.
Step-by-step explanation:
The given rational function is f(x) = (x²+4x-5)/(2x²+4x-16).
To simplify this function, we can factor the numerator and denominator.
Factoring the numerator, we have (x+5)(x-1).
Factoring the denominator, we have 2(x+4)(x-2).
Therefore, the simplified rational function is f(x) = (x+5)(x-1)/(2(x+4)(x-2)).