Could someone show me the steps to get this answer?

confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = (x-9)/(x+5)

g(x) = (-5x-9)/(x-1)

Start with f(x) = (x-9)/(x+5) and g(x) = (-5x-9)/(x-1).  To obtain f(g(x)), throw out each appearance of x in f(x) = (x-9)/(x+5) and replace it with g(x) = (-5x-9)/(x-1):

f(g(x)) = [(-5x-9)/(x-1) - 9] / [(-5x-9)/(x-1) + 5]

Now simplify the algebra.  If your result equals just x, then you have proven that f and g are inverses of one another.  Need help with the fractions?  If so, do what you can and share it here; I'd then be glad to give you feedback on your work.