Final answer:
The expression X²-4/x³ divided by xµ-2x´/x+4 is simplified by first converting the division to multiplication by the reciprocal and then using division of exponentials to subtract exponents of like bases. The simplified form is obtained by canceling common factors and applying arithmetic.
Step-by-step explanation:
To simplify the expression X²-4/x³ divided by xµ-2x´/x+4, we need to perform a few steps involving division of exponentials and simplification of the given expressions. Let's start by re-writing the division as multiplication by the reciprocal of the divisor:
(X² - 4) / x³ × (x + 4) / (xµ - 2x´)
Now, we can simplify the expression by cancelling any common factors and applying the rules for division of exponentials, which involves subtracting the exponents of like bases. In this case, we can simplify x terms by subtracting exponents:
X² / xµ = x² - µ = x²-5 = 1/x³
-4 / (-2x´) simplifies to 2/x´
After simplifying, we have:
((1/x³ + 2/x´) × (x + 4))
This is the simplified expression using the division of exponentials and the rules of arithmetic.