Perform the subtraction.
(4x/x^2+2x-8)-(x/x^2-16)
To perform the subtraction of the given expressions:
1. First, factorize the denominators of both fractions to simplify the expression.
For the first fraction, x^2 + 2x - 8, it can be factored as (x+4)(x-2).
For the second fraction, x^2 - 16, it can be factored as (x+4)(x-4).
2. Rewrite the expression using the factored denominators:
(4x/(x+4)(x-2)) - (x/(x+4)(x-4))
3. Since the denominators are now the same, we can combine the numerators:
[(4x - x)/(x+4)(x-2)]
4. Simplify the numerator:
(3x)/(x+4)(x-2)
Therefore, the final result of the subtraction is 3x/(x+4)(x-2).