taking it exactly the way you wrote it, the LCD is 2x
(1/2)x - (3/x) + 6
= ( x^2 - 6 + 2x)/(2x)
If you meant
1/(2x) - 3/(x+6) it would be different, but I don't want to guess what you mean
BTW, I would classify the opening expression as simplified enough.
Simplify 1/2x-3/x+6
2 answers
Last term in the numerator should have been 12x
( x^2 - 6 + 12x)/(2x)
( x^2 - 6 + 12x)/(2x)