Find the Holes in the Graph f(x)=(x+3)/((x-4)(x+3))

$f (x) = \frac{x + 3}{(x - 4) (x + 3)}$

Step 1

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$f (x) = \frac{x + 3}{(x - 4) (x + 3)}$

Rewrite the expression.

$f (x) = \frac{1}{x - 4}$

Step 2

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

$x + 3$

Step 3

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $\frac{1}{x - 4}$ .

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Substitute $- 3$ for $x$ in $\frac{1}{x - 4}$ and simplify.

Substitute $- 3$ for $x$ to find the $y$ coordinate of the hole.

$\frac{1}{- 3 - 4}$

Simplify.

Subtract $4$ from $- 3$ .

$\frac{1}{- 7}$

Move the negative in front of the fraction.

$- \frac{1}{7}$

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

$(- 3, - \frac{1}{7})$

Step 4