Question 55
For nonzero real numbers $a$ and $b$, $a \neq -1$ and $b \neq -1$, we have
$$
\frac{a}{b+1} + \frac{b}{a+1} = 1.
$$
Which statement about the expression
$$
\frac{a}{b} + \frac{b}{a} - \frac{1}{ab}
$$
is correct?
(A) The expression can take any value from the interval $(0,1]$.
(B) The expression can take any value from 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.
$$
\frac{a}{b+1} + \frac{b}{a+1} = 1.
$$
Which statement about the expression
$$
\frac{a}{b} + \frac{b}{a} - \frac{1}{ab}
$$
is correct?
(A) The expression can take any value from the interval $(0,1]$.
(B) The expression can take any value from 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.