$\displaystyle
\tan(A + B)={-7/6},
\tan(B)={5/3}
$
Find tan(A)
$\displaystyle \tan(a+b) = \frac{\tan{a} + \tan{b}}{1 - \tan{a}\tan{b}}$
$\displaystyle \tan(a+b) (1 - \tan{a}\tan{b}) = \tan{a} + \tan{b}$
$\displaystyle \tan(a+b) - \tan(a+b) \tan{a} \tan{b} = \tan{a} + \tan{b}$
$\displaystyle \tan(a+b) - \tan{b} = \tan{a} - \tan(a+b) \tan{a} \tan{b}
$
$\displaystyle \tan(a+b) - \tan{b} = \tan{a}[1 - \tan(a+b) \tan{b}]$
$\displaystyle \frac{\tan(a+b) - \tan{b}}{1 - \tan(a+b) \tan{b}} = \tan{a}$