Answer
proof below.
Work Step by Step
This is a direct proof, so we go from assumption toward result using definitions.
Let $x$ be an irrational number. Then it cannot be expressed as $\frac{m}{n}$ for any two integers $m$ and $n$. Instead, represent $x$ in simplest form as $\frac{a}{b}$, where either $a$, $b$, or both are not integers. $1/x$ is thus $\frac{b}{a}$. Because $x=\frac{a}{b}$ was in its simplest form, there is no common factor to remove from $\frac{b}{a}$. Because $a$ and $b$ are not both integers, $1/x$ is irrational.
