Find the Holes in the Graph ((x+2)(x-2))/((x+2)(x-5))

$\frac{(x + 2) (x - 2)}{(x + 2) (x - 5)}$

Step 1

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{(x + 2) (x - 2)}{(x + 2) (x - 5)}$

Rewrite the expression.

$\frac{x - 2}{x - 5}$

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 $\frac{x - 2}{x - 5}$ .

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Substitute $- 2$ for $x$ in $\frac{x - 2}{x - 5}$ and simplify.

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

$\frac{- 2 - 2}{- 2 - 5}$

Simplify.

Subtract $2$ from $- 2$ .

$\frac{- 4}{- 2 - 5}$

Subtract $5$ from $- 2$ .

$\frac{- 4}{- 7}$

Dividing two negative values results in a positive value.

$\frac{4}{7}$

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

$(- 2, \frac{4}{7})$

Step 4