Okay so I'm trying to verify the following identity: $\displaystyle \frac{\tan^2\theta-1}{3\tan^2\theta+2\tan\theta-1}=\frac{\tan\theta-1}{3\tan\theta-1}$

Working on the right hand side I did this: $\displaystyle \frac{\tan\theta-1}{3\tan\theta-1}*\frac{\tan\theta+1}{\tan\theta+1}$

and that works out to be: $\displaystyle \frac{\tan^2\theta-1}{3\tan^2\theta+2\tan\theta-1}$

Am I even allowed to do what I did?