Math Problems: f(x) = 1/x - f((x-1)/x)

Given:
f(x) = 1/x - f((x-1)/x), a real valued function such that x is not equal to 0 or 1,
f(-4) = n/m
What is the sum of n and m if they are coprime?

Answer: 119

Solution:
f(-4) = (-1/4) - f(5/4)
f(5/4) = (4/5) - f(1/5)
f(1/5) = 5 - f(-4)

2(f(-4)) = 79/20
f(-4) = 79/40

79 + 40 = 119