Final Answer:
The simplified expression is (-1/2)(x-4)(x+4)/(x^2).
Step-by-step explanation:
We are given the expression {4-x}/{4+x}\{2x}{x²} -16 and we need to simplify it. We can start by factoring the denominator of the first fraction as (4+x) and the denominator of the second fraction as 2x*x^2 = 2x^3. This gives us:
(4-x)/(4+x) * 1/(2x^3) - 16
Next, we can combine the two fractions by finding a common denominator, which is 2x^3(4+x). This gives us:
(4-x)(2x^3) / [(4+x) * 2x^3] - 16(2x^3)(4+x) / [(4+x) * 2x^3]
Simplifying this expression, we get:
(-2x^2)(x-4)(x+4) / [(4+x) * 2x^3]
Finally, we can cancel out the common factor of 2x^2 in the numerator and denominator to get the simplified expression:
(-1/2)(x-4)(x+4)/(x^2)
Therefore, the simplified expression is (-1/2)(x-4)(x+4)/(x^2).