Find the Holes in the Graph y=(x-2)/((x+2)(x-2))

$y = \frac{x - 2}{(x + 2) (x - 2)}$

Step 1

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$y = \frac{x - 2}{(x + 2) (x - 2)}$

Rewrite the expression.

$y = \frac{1}{x + 2}$

Step 2

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

$x - 2$

Step 3

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $\frac{1}{x + 2}$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Substitute $2$ for $x$ in $\frac{1}{x + 2}$ and simplify.

Substitute $2$ for $x$ to find the $y$ coordinate of the hole.

$\frac{1}{2 + 2}$

Add $2$ and $2$ .

$\frac{1}{4}$

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

$(2, \frac{1}{4})$

Step 4