SOLUTION: Prove that if 0 < a < 1 and 0 < b < 1, then 0 < a + b

SOLUTION: Prove that if 0 < a < 1 and 0 < b < 1, then 0 < a + b - ab < 1.

Question 457927: Prove that if 0 < a < 1 and 0 < b < 1, then 0 < a + b - ab < 1.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Take note that

(a factoring technique I've heard as "Simon's Favorite Factoring Trick" on a math website but I don't know if it really has a name). The numbers a-1 and b-1 range between -1 and 0, so

Add 1 to both sides:

and we are done.
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