( tan 70 + tan 65 ) / ( 1 - tan 70 tan 65 ) =

This is a tan (u+v) example:
tan (u+v) = (tan u + tan v) / (1 - tanu * tan v)

Substituting u = 70 and v = 65:
( tan 70 + tan 65 ) / ( 1 - tan 70 tan 65 ) = tan (70 + 65)

This equals
tan (135) = tan(3pi/4) = -1

( tan A + tan B) /(1 - tan A tan B) = tan(A + B)

=> [ tan(70) + tan(65) ] /[ 1 - tan(70)tan(65)] = tan(70 + 65)

= tan(135)

= tan(180 - 45)

= -tan(45)

= -1