Find the Holes in the Graph y=x/(x(x-1))

$y = \frac{x}{x (x - 1)}$

Cancel the common factor of $x$ .

Cancel the common factor.

$y = \frac{x}{x (x - 1)}$

Rewrite the expression.

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

To find the holes in the graph, look at the denominator factors that were cancelled.

$x$

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $\frac{1}{x - 1}$ .

Set $x$ equal to $0$ .

$x = 0$

Substitute $0$ for $x$ in $\frac{1}{x - 1}$ and simplify.

Substitute $0$ for $x$ to find the $y$ coordinate of the hole.

$\frac{1}{0 - 1}$

Simplify.

Subtract $1$ from $0$ .

$\frac{1}{- 1}$

Divide $1$ by $- 1$ .

$- 1$

The holes in the graph are the points where any of the cancelled factors are equal to $0$ .

$(0, - 1)$