Final answer:
To simplify the rational expression (6x-24)/(16-x^2), factor the numerator and denominator. Cancel out the common factor of (x-4) to simplify the expression to (6(x-4))/(4+x).
Step-by-step explanation:
To simplify the rational expression (6x-24)/(16-x^2), we need to factor the numerator and denominator.
- Factor 6x-24: 6(x-4).
- Factor 16-x^2 as the difference of squares: (4+x)(4-x).
Now we can cancel out the common factor of (x-4) and simplify the expression to:
(6(x-4))/(4+x)