Verified answer

(x - 4/x) / (2/x + 1)

First multiply the whole equation by x/x to get rid if the denominators, leaving:

[x (x - 4/x)] / [x (2/x + 1)]

[x(x) - 4] / [2 + x]

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

[(x +2)(x - 2)] / (x + 2)

The (x + 2)'s cancel each other out, leaving:

x - 2

:)

= ([x - {4/x}]/[2/x]) + 1

= ([{x² - 4}/x][x/2]) + 1

= ([x² - 4]/2) + 1

= (x² - 4 + 2)/2

= (x² - 2)/2

Answer: (x² - 2)/2 OR 1/2(x² - 2)