5/z+4 + 3/3z+12

I can figure out that the LCM is z+4. But the answer to the problem is 6/z+4. At some point I have an idea that I multiply the 3 in the second expression by 3 to get 9, and then multiply it by -1 to get -9. Then (or before that) I multiply 5 by 3 to get 15. That would give me the answer but I just can't seem to get there the right way without basically making up my own rules.

Help is appreciated more than words can say. I'm ready to pull my hair out over these problems.