When evaluating the limit (1/2 - 1/x) * (1/ (x-2)) as x→2, how's (1/2 - 1/x) simplified to (x-2)/(2x)

I get how to evaluate it by plugging in 1.999 to x for example, but my answer sheet shows a simpler way which I don't quite understand. Thanks.

(1/2 - 1/x) simplified to (x - 2)/2x by doing algebraic subtraction...just a lie little knowledge of LCM

and if use ask about the limit stuff then ans is 1/4

1/2-1/x. Get a common denominator = 2x

X/(2x)-2/(2x)= (x-2)/(2x)

So (1/2-1/x)(1/(x-2)=(x-2)/(2x) * 1/(x-2)

= 1/(2x)

Now if you plug in x->2, the limit is 1/4

Hoping this helps!