Çözüldü Integers - Two-Variable Linear Equations (7th Grade)

If a and b are integers, and 1 / (a - b) + 2 / (a + b) = 1, then what is the maximum product of a and b?

A) 0
B) 3
C) 6
D) 9
E) 12

It is immediately observed that if a - b = 2....(I) and a + b = 4....(II) then the condition 1 / 2 + 1 / 2 = 1 is satisfied.
Summing the equations (I) and (II) side by side 2a = 4 ⇒ a = 3....(III)
Substituting the value in (III) for (I) [ or (II) ], b = 3 - 1 = 1....(IV)
a·b = 3·1 = 3.

Note: The values a = 3 and b = 0 also give the result 1, but their product is zero.

Original Question (Turkish): https://matematiknotu.com/wp-content/uploads/2020/11/Test-07-Rasyonel-Sayilar-I.pdf
(Son soru)