F(x) and g(x) are functions. If f(x) = x^2 - 1 and f/g(x) = (x+1)^2, find g(x)

I'm stumped! Please show me how to do this>

f/g(x) = (x+1)^2
Multiply both sides by g(x):
f(x) = (x+1)^2 (g(x))
Substitute what's given for f(x):
x^2 - 1 = (x+1)^2 (g(x))
Divide by (x+1)^2
g(x) = (x^2 - 1) / (x+1)^2
Cancel the common factor (x+1):
g(x) = (x - 1) / (x + 1)