Final answer:
To simplify the rational expression (x²-16)/(x+7)-(x+8)/(x-3), we first find a common denominator and then expand and simplify the expression.
Step-by-step explanation:
To simplify the rational expression (x²-16)/(x+7)-(x+8)/(x-3), we first need to find a common denominator for the two fractions. The common denominator is (x+7)(x-3), so we can write the expression as:
((x²-16)(x-3) - (x+8)(x+7))/((x+7)(x-3))
Expanding and simplifying this expression, we get:
(x³ - 17x - 120)/((x+7)(x-3))