### Instruction: If $\tan x = 2,$ then find $\tan \left( x + \frac{\pi}{4} \right).$.### Response: I know that there is a formula for the tangent of a sum of angles, which is $\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}.$
I can use this formula with $A = x$ and $B = \frac{\pi}{4},$ and substitute the given value of $\tan x = 2.$
I get $\tan \left( x + \frac{\pi}{4} \right) = \frac{\tan x + \tan \frac{\pi}{4}}{1 - \tan x \tan \frac{\pi}{4}}.$
Now I need to recall the value of $\tan \frac{\pi}{4},$ which I know is 1.
I can plug that in and simplify the fraction.