Question:
Prove or disprove this statement
Consider the statement that if a and b are real numbers in the open interval (0, 1), then a/[b(1 - a)] > 1.
[Note: To say that a and b are in the open interval (0, 1) means that 0 < a < 1 and 0 < b < 1.]
Either prove this statement (that is, prove that it's true for all real numbers a, b in the open interval (0, 1)) or give a counterexample (that is, give specific real numbers a, b such that a/[b(1 - a)] <= 1).