expand (2/x - x/2)^4

To expand the expression (2/x - x/2)^4, we can use the binomial theorem, which states that (a - b)^n = Σ (n choose k) * a^(n-k) * b^k, where the sum is from k=0 to n.

Here, a = 2/x, b = x/2, and n = 4.

So, (2/x - x/2)^4 =

(4 choose 0) * (2/x)^4 * (x/2)^0 - (4 choose 1) * (2/x)^3 * (x/2)^1 + (4 choose 2) * (2/x)^2 * (x/2)^2 - (4 choose 3) * (2/x)^1 * (x/2)^3 + (4 choose 4) * (2/x)^0 * (x/2)^4

= 1 * 16/x^4 * 1 - 4 * 8/x^3 * x/2 + 6 * 4/x^2 * x^2/4 - 4 * 2/x * x^3/8 + 1 * 1 * x^4/16

= 16/x^4 - 16/x^2 + 6 - 16x^2 + x^4/16

So, (2/x - x/2)^4 = 16/x^4 - 16/x^2 + 6 - 16x^2 + x^4/16.