Question

What should be added to $\frac{1}{x}$ to make it equal to $x$?

• A. $\frac{x^2-x}{x^2}$
• B. $\frac{x}{x^2-1}$
• C. $\frac{x^2+1}{x}$
• D. $\frac{x^2-1}{x}$

Answer 1

The correct option is D $\frac{x^2-1}{x}$

Let the required polynomial be represented by $y$

$\therefore \frac{1}{x}+y=x$

$\therefore y=x-\frac{1}{x}$ = $\frac{x^2-1}{x}$