Question

The additive inverse of $x+\frac{1}{x}$ will be ________.

Answer 1

Given expression is $x+\frac{1}{x}$.

We know that, additive inverse means an addition of a term or expression to the given expression, such that their sum equals to zero.

Let $P$ be such an expression.

Hence, $x+\frac{1}{x}+P=0$

$\Rightarrow P=-x-\frac{1}{x}$.

Hence, the additive inverse of $x+\frac{1}{x}$ is $-x-\frac{1}{x}$.