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MathNet 2016-part-05 — 184 problems (EN–VI) Question 79

Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)

Question 79

Non-zero real numbers $a$ and $b$ satisfy $\frac{a}{b+1} + \frac{b}{a+1} = 1$. Which of the statements about the expression $\frac{a}{b} + \frac{b}{a} - \frac{1}{ab}$ is correct?
(A) The expression can take any value in the interval $(0, 1]$.
(B) The expression can take any value in the interval $[1, 2)$.
(C) The value of the expression is 1.
(D) The value of the expression is 2.
(E) We cannot say anything about the value of the expression.