Question

# What will be the additive inverse of $x + \dfrac{1}{x}$?

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Hint – In this question we have to find the additive inverse of given expression, an expression when added to a given expression is equal to 0. If A is an expression and if $\overline {\text{A}}$ is the additive inverse then${\text{A + }}\overline A = 0$. Use this concept to get the right answer.

$x + \dfrac{1}{x}$
$\Rightarrow A + x + \dfrac{1}{x} = 0$
$\Rightarrow A = - x - \dfrac{1}{x}$
Hence the required additive inverse of the given expression is $- x - \dfrac{1}{x}$.