My textbook gives these two equations including the real interest rate and says that the second equation (b) can be arrived at from the first (a), but doesn't explain how.
rr = Real Interest Rate, r = Nominal Interest Rate, i = Inflation
Equation (a): $$Growth\ in\ Purchasing\ Power=1+r_r = \displaystyle\frac{1+r}{1+i}$$
Equation (b):
$$Real\ Interest\ Rate = r_r = \displaystyle\frac{r-i}{1+i}$$
I'm feeling slightly obtuse but I've been away from math quite a while, and can't figure out how to rearrange the first formula into the second one.
What are the exact equation steps necessary to get from: $ r_r = \displaystyle\frac{1+r}{1+i}-1$ ⇒ $r_r = \displaystyle\frac{r-i}{1+i}$ ?