Simplifying an equation but don't know how to get to (1-beta/beta) term So, a textbook example from macroeconomics. The final equation is given and I'm trying to verify how to reach it. I think my main issue is what technique I should use to get the $(1-\beta/\beta)$ term, or I'm doing something else wrong as well. Any help on how to solve this is greatly appreciated!
The goal equation is:
$i = r + \pi + ((1-\beta)/\beta)(\pi-\mu) + (\eta/\beta)(y-ÿ) $
We start out with equations A and B: A: $\mu - \pi + \ln L^* = \ln k + \eta y - \beta i $
B: $\ln L^* = \ln k +\eta ÿ - \beta(r+\mu) $
Inserting B in A and simplifying a bit:
$\mu-\pi = nÿ-\beta(r+\mu)=\eta y-\beta i $
I rearrange:
$\beta i = \beta(r+\mu)+\eta(y-ÿ)+(\pi-\mu)$
Divide by $\beta$
$i = (r+\mu) + (\eta/\beta)(y-ÿ)+(\pi-\mu)/\beta$
But from here I'm not able to go any further. If  I'm correct this far, the following should be true. But I don't know how to make them equal... 
$(r+\mu) + (\pi+\mu)/\beta = r +\pi+((1-\beta)/\beta)$
A: $\require{cancel}$
After your initial substitution, you should have
$$\mu - \pi + \ln L^* = \ln k + \eta y - \beta i$$
$$\mu - \pi + (\underbrace{\cancel{\ln k} +\eta \ddot y - \beta(r+\mu)}_{\ln L^*}) = \cancel{\ln k} + \eta y - \beta i$$
$$\mu - \pi + \eta \ddot y - \beta(r+\mu) =  \eta y - \beta i$$
$$\beta i  =  \eta y-(\mu - \pi + \eta \ddot y - \beta(r+\mu))$$
$$\beta i  =  \eta y-\mu + \pi - \eta \ddot y + \beta(r+\mu)$$
$$\beta i  =   \pi -\mu + \eta y - \eta \ddot y + \beta(r+\mu)$$
$$\beta i  =   \pi -\mu + \eta(y - \ddot y) + \beta r + \underbrace{\beta\pi - \beta\pi}_0+\beta\mu$$
$$\beta i  =   \pi -\mu + \eta(y - \ddot y) + \beta(r + \pi) - \beta\pi+\beta\mu$$
$$\beta i  = \beta(r + \pi) + \pi -\mu + \eta(y - \ddot y) - \beta\pi+\beta\mu$$
$$\beta i  = \beta(r + \pi) + (\pi -\mu) - \beta(\pi-\mu) + \eta(y - \ddot y)$$
$$\beta i  = \beta(r + \pi) + \underbrace{1\cdot(\pi -\mu) - \beta\cdot(\pi-\mu)}_{\textrm{factor out }\pi-\mu} + \eta(y - \ddot y)$$
$$\beta i  = \beta(r + \pi) + (1-\beta)\cdot(\pi -\mu)  + \eta(y - \ddot y)$$
$$i  = r + \pi + ((1-\beta)/\beta)\cdot(\pi -\mu)  + (\eta/\beta)(y - \ddot y)$$
as desired.
