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How to remove the "if" part following the calculation result obtained from Solve?

Wen Dao
Posted 1 day ago

Solve[ForAll[{x, y}, Equivalent[ m (x/a) + n (y/b) == 1, ((t1 - t2) (b (-1 + t1 t2) x + a (b + b t1 t2 - (t1 + t2) y)))/((1 + t1^2) (1 + t2^2)) == 0]], {m, n}, Reals] // Simplify

enter image description here

The code generates an answer containing "if". How can I remove the "if" part to obtain the result shown in the bottom image?

enter image description here
POSTED BY: Wen Dao
2 Replies
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You can remove the conditions by extracting the first element of the ConditionalExpression:

Solve[ForAll[{x, y}, 
    Equivalent[
     m (x/a) + n (y/b) == 
      1, ((t1 - t2) (b (-1 + t1 t2) x + 
           a (b + b t1 t2 - (t1 + t2) y)))/((1 + t1^2) (1 + t2^2)) == 
      0]], {m, n}, Reals] /. 
  ConditionalExpression -> (#1 &) // Simplify
POSTED BY: Gianluca Gorni
Wen Dao
Wen Dao
Posted 18 hours ago

Thanks for your help!
POSTED BY: Wen Dao
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