Find the Holes in the Graph y=((x-2)(x+5))/((x+5)(x+3))

$y = \frac{(x - 2) (x + 5)}{(x + 5) (x + 3)}$

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$y = \frac{(x - 2) (x + 5)}{(x + 5) (x + 3)}$

Rewrite the expression.

$y = \frac{x - 2}{x + 3}$

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

$x + 5$

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $\frac{x - 2}{x + 3}$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Substitute $- 5$ for $x$ in $\frac{x - 2}{x + 3}$ and simplify.

Substitute $- 5$ for $x$ to find the $y$ coordinate of the hole.

$\frac{- 5 - 2}{- 5 + 3}$

Simplify.

Subtract $2$ from $- 5$ .

$\frac{- 7}{- 5 + 3}$

Add $- 5$ and $3$ .

$\frac{- 7}{- 2}$

Dividing two negative values results in a positive value.

$\frac{7}{2}$

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

$(- 5, \frac{7}{2})$