We can simplify the expression step by step:

Recall the trigonometric identity:

[ \tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} ]

Let A = 80° and B = 55°, then:

[ \tan(80° + 55°) = \frac{\tan 80° + \tan 55°}{1 - \tan 80° \tan 55°} ]

Substitute the values:

[ \tan 135° = \frac{\tan 80° + \tan 55°}{1 - \tan 80° \tan 55°} ]

Simplify the expression:

[ -1 = \frac{\tan 80° + \tan 55°}{1 - \tan 80° \tan 55°} ]

Add 1 to both sides:

[ \frac{\tan 80° + \tan 55°}{1 - \tan 80° \tan 55°} + 1 = 0 ]

So the final expression simplifies to 0.