Algebra · Symmetric expressions · Rational expressions · Conditional identities · Clearing denominators
Let \(a\) and \(b\) be non-zero real numbers with \(a \ne -1\) and \(b \ne -1\), satisfying
\[ \frac{a}{b+1} + \frac{b}{a+1} = 1 . \]
Which of the following statements about the expression \(\dfrac{a}{b} + \dfrac{b}{a} - \dfrac{1}{ab}\) 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 Nothing can be said about the value of the expression.
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2016, 1. letnik, category A, problem A3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source