Expectation of a MM estimator

Question

So I want to calculate the expectation of my estimator to see if it is biased or not. Data:

$\bar{X} = \frac{1}{n}\sum_{i}x_i$

$E[\bar{X}]= \frac{\theta}{\theta + 1}$

$\hat{\theta}_{mm}$ = $\frac{\bar{X}}{1-\bar{X}}$

I apparently calculated it wrong: $E[\hat{\theta}_{mm}]=E[\frac{\bar{X}}{1-\bar{X}}]=\frac{E[\bar{X}]}{1-E[\bar{X}]}$