Answer
$\dfrac{3}{x}$
For this expression, $x$ cannot equal $0$ or $1$.
Work Step by Step
To solve these types of problems, we want to remove greatest common factors in both the numerator and denominator. Hopefully, we will find that
For this problem, in the numerator, we can factor out a $3$, whereas in the denominator, we can factor out an $x$:
$\dfrac{3(x - 1)}{x(x - 1)}$
We can cancel $x - 1$ from both numerator and denominator. We are left with:
$\dfrac{3}{x}$
To see what restrictions for the variable we have, we need to see which values for the variable will make the denominator equal to $0$, which will cause the fraction to become undefined. Let's set the denominator in the original expression equal to $0$ to see which values for the variable we cannot use:
$x^2 - x = 0$
Factor out an $x$ from both terms:
$x(x - 1) = 0$
Using the Zero-Product Property, we can set each factor equal to $0$ and then solve for $x$:
First factor:
$x = 0$
Second factor:
$x - 1 = 0$
Add $1$ to both sides of the equation to isolate the $z$ term:
$x = 1$
For this expression, $x$ cannot equal $0$ or $1$.
