Question

(\frac{x^{2}-4}{2x}div 2 - x=)

Explanation:

Step1: Rewrite division as multiplication

$\frac{x^2 - 4}{2x} \div \frac{2 - x}{1} = \frac{x^2 - 4}{2x} \times \frac{1}{2 - x}$

Step2: Factor the quadratic numerator

$x^2 - 4 = (x-2)(x+2)$, so:
$\frac{(x-2)(x+2)}{2x} \times \frac{1}{2 - x}$

Step3: Rewrite $2-x$ as $-(x-2)$

$\frac{(x-2)(x+2)}{2x} \times \frac{1}{-(x-2)}$

Step4: Cancel common terms $(x-2)$

$\frac{x+2}{2x} \times \frac{1}{-1} = -\frac{x+2}{2x}$

Answer:

$-\frac{x+2}{2x}$ (where $x
eq 0, 2$)