How do I find a common denominator for a complex faction when one denominator is 2m-1 and the other is 2m+5

The best option is to multiply them together, there would be no value that is common between the two, (2m - 1) (2m + 5), and leave it in this form.

However, there is a second method.

Notice how between the two sits a difference of 6.

You can manipulate one of the fractions to render the same denominator and work from there.