Final answer:
To subtract and simplify f(x) - g(x), find a common denominator and combine the fractions. The simplified form is (x^2 - 2)/(x+3)(x-2).
Step-by-step explanation:
To subtract and simplify f(x) - g(x), we first need to find a common denominator for the two fractions. The common denominator is (x + 3)(x - 2). Then, we can rewrite f(x) and g(x) with the common denominator:
f(x) = (x+5)(x-2)/(x+3)(x-2) and g(x) = (5x-7)/(x+3)(x-2)
Next, we can subtract the two fractions:
f(x) - g(x) = (x+5)(x-2)/(x+3)(x-2) - (5x-7)/(x+3)(x-2)
Combining the fractions, we have:
f(x) - g(x) = (x^2+5x-2x-10-5x+7)/(x+3)(x-2)
Simplifying further, we get:
f(x) - g(x) = (x^2 - 2)/(x+3)(x-2)
Therefore, the simplified form of f(x) - g(x) is (x^2 - 2)/(x+3)(x-2). So, the correct option is a) -4x+50/(x^2-5x+6).