# What is the opposite and reciprocal of -1/x?

Mar 21, 2018

The opposite reciprocal of $- \frac{1}{x}$ is $x$.

#### Explanation:

The definition of two opposite reciprocal numbers means that their product is $- 1$.

So we can set up an equation with two numbers (one of them is $- \frac{1}{x}$ and the other we'll call $y$) and multiply them together, and set them equal to $- 1$:

$- \frac{1}{x} \cdot y = - 1$

$\frac{1}{x} \cdot y = 1$

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

$\textcolor{w h i t e}{y} = \frac{1}{1} \cdot \frac{x}{1}$

$\textcolor{w h i t e}{y} = 1 \cdot x$

$\textcolor{w h i t e}{y} = x$

That's the opposite reciprocal. Hope this helped!