1/9 -K+3/72k = 1/9k - k-1/8k

i can't figure out how to get rid of the denominators

It is very important to use brackets.

I will assume you meant

1/9 -(K+3)/(72k) = 1/(9k) - (k-1)/(8k)

multiply each term by 72k to get

72k - (k-3) = 8 - (k-1)

I am sure you can take it from there.