设tan(α+β)=2/5,tan(β-π/4)=1/4,则tan(α+π/4)的值

C.3/22
tan[A+(π/4)]=tan{(A+B)-[B-(π/4)]}
tan{(A+B)-[B-(π/4)]}
={tan(A+B)-tan[B-(π/4)]}/{1+〈tan{(A+B)×tan[B-(π/4)]〉}
=[(2/5)-(1/4)]/[1+(2/5)×(1/4)]
=(3/20)/(22/20)
=3/22