Question 4
Find $a+b$ given
$$\left(\frac{1/a}{1/a-1/b}-\frac{1/b}{1/a+1/b}\right)\left(\frac1a-\frac1b\right)\frac1{1/a^2+1/b^2}=\frac23.$$
Original choices: (A) $1$; (B) $2$; (C) $3$; (D) $4$; (E) $5$.
Source-data warning: the printed condition lacks a restriction needed for a uniquely determined requested answer. Keep the original condition and options; explain whether a unique value follows, using valid examples or counterexamples. This item is assessed manually.
$$\left(\frac{1/a}{1/a-1/b}-\frac{1/b}{1/a+1/b}\right)\left(\frac1a-\frac1b\right)\frac1{1/a^2+1/b^2}=\frac23.$$
Original choices: (A) $1$; (B) $2$; (C) $3$; (D) $4$; (E) $5$.
Source-data warning: the printed condition lacks a restriction needed for a uniquely determined requested answer. Keep the original condition and options; explain whether a unique value follows, using valid examples or counterexamples. This item is assessed manually.