$\displaystyle f(x : \theta)=\frac{\theta}{(x+\theta)^{2}} , \ \ \ H_{0}:\theta=1, \ \ \ H_{1}:\theta=2 $

Mr F edit:Additional information given to me via pm:

x>0, theta>0, is an unknown parameter.

find the likelihood ratio test .

and show the probability of TYPE II error is

19/21