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

Question

f(x) = (x-7)/(x+3) and g(x) = (-3x-7)/(x-1)

I got to the point where f(g(x)) is plugged in but how would I simplify it?

(((-3x-7)/(x-1))-7)/(((-3x-7)/(x-1)+3)