Question

Solve for $x$ in $\frac{x}{b}+\frac{b}{x}=\frac{a}{b}+\frac{b}{a}$.

• A. $-a$ or $\frac{-b^2}{a}$
• B. $-a$ or $-\frac{b^2}{a}$
• C. $-a$ or $\frac{b^2}{a}$
• D. $a$ or $\frac{b^2}{a}$

Answer 1

The correct option is D $a$ or $\frac{b^2}{a}$

By transposition, we get
$\frac{x}{b}-\frac{a}{b}=\frac{b}{a}-\frac{b}{x}$
or $\frac{x-a}{b}=\frac{b(x-a)}{ax}$ or $\frac{1}{b}(x-a)=\frac{b}{ax}(x-a)$ or $(x-a)(\frac{1}{b}-\frac{b}{ax})=0$
$\therefore x-a=0$ or $\frac{1}{b}=\frac{b}{ax}$
i.e., $x=a$ or $x=\frac{b^2}{a}$