Find the Excluded Values (x-2)/((x+9)(x-5))

$\frac{x - 2}{(x + 9) (x - 5)}$

Step 1

Set the denominator in $\frac{x - 2}{(x + 9) (x - 5)}$ equal to $0$ to find where the expression is undefined.

$(x + 9) (x - 5) = 0$

Step 2

Solve for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 9 = 0$

$x - 5 = 0$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

Set $x - 5$ equal to $0$ and solve for $x$ .

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

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

The final solution is all the values that make $(x + 9) (x - 5) = 0$ true.

$x = - 9, 5$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = - 9, x = 5$

Step 4

Find the Excluded Values (x-2)/((x+9)(x-5))

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