If $\displaystyle {\tan{\alpha}}=\frac{{1}}{{2}}$ such that $\displaystyle \alpha$ terminates in quadrant I and $\displaystyle {\tan{\beta}}=-\frac{{1}}{{2}}$ such that $\displaystyle \beta$ terminates in quadrant IV then

 $\displaystyle {\tan{{\left(\alpha+\beta\right)}}}=$Preview Question 6  

Your answer should be exact but you do not have to rationalize your denominator.