h(x)= x/(x-2) and g(x)= 2/x. Find and simplify

Question

h of g(x).

I plugged g(x) into h:
h(x)= (2/x)/[(2/x)-2]

Now, would I multiply each by x, the Common Denominator?
Therefore getting 2/(2-2x) which simplifies to 1-x?

Answer 1

2/(2-2x) is correct, but when simplified gives 1/(1-x).

Answer 2

Ah, that was a stupid mistake on my part. I blame the late hour...
Thank you for your help, have a good night!=)

Answer 3

You're welcome! Get some sleep!