Find the Holes in the Graph h(x)=x/(x(x-3))

$h (x) = \frac{x}{x (x - 3)}$

Step 1

Cancel the common factor of $x$ .

Cancel the common factor.

$h (x) = \frac{x}{x (x - 3)}$

Rewrite the expression.

$h (x) = \frac{1}{x - 3}$

Step 2

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

$x$

Step 3

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $\frac{1}{x - 3}$ .

Set $x$ equal to $0$ .

$x = 0$

Substitute $0$ for $x$ in $\frac{1}{x - 3}$ and simplify.

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

$\frac{1}{0 - 3}$

Simplify.

Subtract $3$ from $0$ .

$\frac{1}{- 3}$

Move the negative in front of the fraction.

$- \frac{1}{3}$

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

$(0, - \frac{1}{3})$

Step 4