Question

A rational expression that will be undefined at x=1?

Answer 1

This rational. expression will be undefined when x=1. 3x+2÷(-x+1)

Answer 2

A rational expression of the form 
$r(x)= \dfrac{p(x)}{q(x)}$
will be undefined for the zeros of the expression $q(x)$. For an expression with a zero equal to 1, the simplest way is to use $(x-1)$ as a factor in $q(x)$. In can be your only one, or you can mix in other factors.

But, so long as the denominator of $r(x)$ is equal to zero, as it is when $q(x)=x-1$, the expression will be undefined at that point x, because it would involve division by zero.

You could use as your sample:

$\dfrac{x-7}{x-1}$

You can try to get fancy and square some factors or add in some radicals or trigonometric functions or anything else, so long as the 1 makes the denominator equal to zero!