Method of moment estimate of: $\frac{\theta}{\theta +1}=\bar{y}$

Question

I am working on mathematical statistical with applications by Todd (5th edition). Currently learning the method of moments, and I am stuck on this simple re-arrangement:

$$\frac{\theta}{\theta +1}=\bar{y}$$

$\bar{y}$ is when setting $\frac{1}{n}\sum_{i=1}^ny_i$

Which implies that the method of moments estimate for $\theta$ is

$$\theta_e = \frac{\bar{y}}{1-\bar{y}}$$

I seem to be missing the trick here as I cannot get the following re-arranged equation above ($\theta_e$), unless it is derived by other means?

Answer 1

Managed to figure the logic out!:

$$\frac{\theta}{\theta +1}=\bar{y} \implies \theta =\bar{y}(1-\theta) \implies \theta = \bar{y} -\bar{y}\theta\implies \bar{y}\theta=\bar{y}-\theta \implies \bar{y}-\theta -\bar{y}\theta\implies\theta (1-\bar{y}) = \bar{y} \implies \theta_e=\frac{\bar{y}}{1-\bar{y}}$$