Question

What must be added to $\frac{x}{y}$ to make it $\frac{y}{x}$?

• A. $\frac{y^2-x^2}{yx}$
• B. $\frac{y-x}{y^2{x}^2}$
• C. $\frac{xy}{x+y}$
• D. $\frac{x^2-y^2}{x^2+y^2}$

Answer 1

The correct option is A $\frac{y^2-x^2}{yx}$

Let $k$ be the required term which needs to be added to $\frac{x}{y}$ to make it equal to $\frac{y}{x}$.
$\frac{x}{y}+k=\frac{y}{x}$
$\Rightarrow k=\frac{y}{x}-\frac{x}{y}=\frac{y^2-x^2}{yx}$
$\therefore$ $\text{Term which needs to be added =}\frac{y^2-x^2}{yx}$