Find the Holes in the Graph f(x)=(5x+15)/(x+3)

$f (x) = \frac{5 x + 15}{x + 3}$

Step 1

Factor $5$ out of $5 x + 15$ .

Factor $5$ out of $5 x$ .

$f (x) = \frac{5 (x) + 15}{x + 3}$

Factor $5$ out of $15$ .

$f (x) = \frac{5 x + 5 \cdot 3}{x + 3}$

Factor $5$ out of $5 x + 5 \cdot 3$ .

$f (x) = \frac{5 (x + 3)}{x + 3}$

Step 2

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$f (x) = \frac{5 (x + 3)}{x + 3}$

Divide $5$ by $1$ .

$f (x) = 5$

Step 3

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

$x + 3$

Step 4

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $5$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Because the cancelled expression is constant with respect to $x$ , it is the $y$ coordinate for every hole.

$5$

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

$(- 3, 5)$

Step 5