Partial fractions (How do I get from x to y)

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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?

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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)

$$\frac{\gamma \lambda_0 w}{\lambda_0 w - \lambda_2(1+r)^t}$$