Final answer:
To subtract and simplify the given expression, find a common denominator, combine the fractions, and simplify the result.
Step-by-step explanation:
To subtract and simplify the given expression, we need to find a common denominator and combine the fractions. The common denominator for the two fractions is (x-2)(x+7)(x+8). We can then multiply the numerators by the appropriate factors to get:
(3(x+7))/((x-2)(x+7)(x+8)) - (7(x-2))/((x+7)(x+7)(x+8))
Next, we can combine the fractions by subtracting the fractions with the same denominator. Simplifying the numerator gives us:
(3x+21 - 7x+14)/((x-2)(x+7)(x+8))
Combining like terms in the numerator gives us:
(-4x+35)/((x-2)(x+7)(x+8))
Therefore, the simplified result is (-4x+35)/((x-2)(x+7)(x+8)).