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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.

Complete step-by-step answer:
Given equation is
$x + \dfrac{1}{x}$
Now we have to find out the additive inverse of this equation.
According to the property of additive inverse, addition of a term or expression to the given expression, such that their sum equals to zero.
Let A be such an expression.
Therefore according to the property of additive inverse the sum of A and the given expression must be zero.
$ \Rightarrow A + x + \dfrac{1}{x} = 0$
Now simplify the above equation we have,
$ \Rightarrow A = - x - \dfrac{1}{x}$
Hence the required additive inverse of the given expression is $ - x - \dfrac{1}{x}$.
So, this the required additive inverse.

Note – Whenever we face such type of problem the key concept involved is to have the basic understanding of additive inverse. The equation for additive inverse mentioned in the hint will help you get on the right track to reach the solution for these kinds of problems.