Find the Holes in the Graph (x+3)/(-3x^2-9x)

$\frac{x + 3}{- 3 x^{2} - 9 x}$

Factor $3 x$ out of $- 3 x^{2} - 9 x$ .

Factor $3 x$ out of $- 3 x^{2}$ .

$\frac{x + 3}{3 x (- x) - 9 x}$

Factor $3 x$ out of $- 9 x$ .

$\frac{x + 3}{3 x (- x) + 3 x (- 3)}$

Factor $3 x$ out of $3 x (- x) + 3 x (- 3)$ .

$\frac{x + 3}{3 x (- x - 3)}$

Cancel the common factor of $x + 3$ and $- x - 3$ .

Factor $- 1$ out of $x$ .

$\frac{- 1 (- x) + 3}{3 x (- x - 3)}$

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{- 1 (- x) - 1 (- 3)}{3 x (- x - 3)}$

Factor $- 1$ out of $- 1 (- x) - 1 (- 3)$ .

$\frac{- 1 (- x - 3)}{3 x (- x - 3)}$

Cancel the common factor.

$\frac{- 1 (- x - 3)}{3 x (- x - 3)}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

$- x - 3$

To find the coordinates of the holes, set each factor that was cancelled equal to $0$ , solve, and substitute back in to $- \frac{1}{3 x}$ .

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

$- x - 3 = 0$

Solve $- x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$- x = 3$

Divide each term in $- x = 3$ by $- 1$ and simplify.

Divide each term in $- x = 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3}{- 1}$

Divide $x$ by $1$ .

$x = \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$x = - 3$

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

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

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

Simplify.

Multiply $3$ by $- 3$ .

$- \frac{1}{- 9}$

Move the negative in front of the fraction.

$- - \frac{1}{9}$

Multiply $- - \frac{1}{9}$ .

Multiply $- 1$ by $- 1$ .

$1 (\frac{1}{9})$

Multiply $\frac{1}{9}$ by $1$ .

$\frac{1}{9}$

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

$(- 3, \frac{1}{9})$

Find the Holes in the Graph (x+3)/(-3x^2-9x)

Related Questions

Support LCMGCF.com by disabling your adblocker.