how do I get from
$$\gamma * \left( \frac{\frac{\lambda_0 w}{(1+r)^t \beta^t \alpha}}{\frac{\lambda_0 w}{(1+r)^t \beta^t \alpha}-\frac{\lambda_2}{\beta^t \alpha}} \right)$$
to $$\frac{\gamma r w \lambda_0 \beta^t}{w \lambda_0\beta^t - \lambda_2(\beta(r+1))^t}$$
Im stuck. Any help?
All terms contain $\alpha$ in the denominator, up and down, so these cancel right away. The same holds for the $\beta^t$
Write $$\lambda_2 = \frac{\lambda_2 \cdot (1+r)^t}{ (1+r)^t}$$
The difference of fractions below then becomes
$$\frac{\lambda_0 \cdot w - \lambda_2 \cdot (1+r)^t}{(1+r)^t }$$
So the total becomes (as now both fractions have the same denominator)
$$\frac{\gamma \lambda_0 w}{\lambda_0 w - \lambda_2(1+r)^t}$$