Final answer:
The difference between the fractions 8/x²+x - 6/x²-4. The difference is (2x-28)/(x²(x+2)(x-2)).
Step-by-step explanation:
To find the difference between the fractions, we need to have a common denominator.
The common denominator for the two fractions is x²(x+2)(x-2).
Multiplying the first fraction by (x-2)/(x-2) and the second fraction by (x+2)/(x+2), we get:
8(x-2)/(x²(x+2)(x-2)) - 6(x+2)/(x²(x+2)(x-2))
Simplifying further, we have: (8x-16)/(x²(x+2)(x-2)) - (6x+12)/(x²(x+2)(x-2))
Combining the terms, we get: (8x-6x-16-12)/(x²(x+2)(x-2))
Simplifying the numerator gives: (2x-28)
Thus, the difference is (2x-28)/(x²(x+2)(x-2)).