Question

State whether the following expression is a polynomial in one variable or not. Give reasons for your answer.

$x-\frac{1}{x}$

Answer 1

First of all you need to know what a polynomial needs to have to be called a polynomial. 
A polynomial need to have the power of it's variables  as whole numbers, i.e non-negative. We can write $x- \frac{1}{x}$ as $x + x^{-1}$. So this is correct that this is an expression with one variable [only x].  But since it has a (-1) power over x, it is not a polynomial.