Find the Excluded Values (8x-16)/(x^2-13x+22)

$\frac{8 x - 16}{x^{2} - 13 x + 22}$

Step 1

Set the denominator in $\frac{8 x - 16}{x^{2} - 13 x + 22}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 13 x + 22 = 0$

Step 2

Solve for $x$ .

Factor $x^{2} - 13 x + 22$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $22$ and whose sum is $- 13$ .

$- 11, - 2$

Write the factored form using these integers.

$(x - 11) (x - 2) = 0$

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

$x - 11 = 0$

$x - 2 = 0$

Set $x - 11$ equal to $0$ and solve for $x$ .

Set $x - 11$ equal to $0$ .

$x - 11 = 0$

Add $11$ to both sides of the equation.

$x = 11$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $(x - 11) (x - 2) = 0$ true.

$x = 11, 2$

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 $0$ .

$x = 2, x = 11$

Step 4

Find the Excluded Values (8x-16)/(x^2-13x+22)

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