Find Where Undefined/Discontinuous (y^2-22y+121)/(2y^2-16y-66)

$\frac{y^{2} - 22 y + 121}{2 y^{2} - 16 y - 66}$

Step 1

Set the denominator in $\frac{y^{2} - 22 y + 121}{2 y^{2} - 16 y - 66}$ equal to $0$ to find where the expression is undefined.

$2 y^{2} - 16 y - 66 = 0$

Step 2

Solve for $y$ .

Factor the left side of the equation.

Factor $2$ out of $2 y^{2} - 16 y - 66$ .

Factor $2$ out of $2 y^{2}$ .

$2 (y^{2}) - 16 y - 66 = 0$

Factor $2$ out of $- 16 y$ .

$2 (y^{2}) + 2 (- 8 y) - 66 = 0$

Factor $2$ out of $- 66$ .

$2 y^{2} + 2 (- 8 y) + 2 \cdot - 33 = 0$

Factor $2$ out of $2 y^{2} + 2 (- 8 y)$ .

$2 (y^{2} - 8 y) + 2 \cdot - 33 = 0$

Factor $2$ out of $2 (y^{2} - 8 y) + 2 \cdot - 33$ .

$2 (y^{2} - 8 y - 33) = 0$

Factor.

Factor $y^{2} - 8 y - 33$ 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 $- 33$ and whose sum is $- 8$ .

$- 11, 3$

Write the factored form using these integers.

$2 ((y - 11) (y + 3)) = 0$

Remove unnecessary parentheses.

$2 (y - 11) (y + 3) = 0$

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

$y - 11 = 0$

$y + 3 = 0$

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

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

$y - 11 = 0$

Add $11$ to both sides of the equation.

$y = 11$

Set $y + 3$ equal to $0$ and solve for $y$ .

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

$y + 3 = 0$

Subtract $3$ from both sides of the equation.

$y = - 3$

The final solution is all the values that make $2 (y - 11) (y + 3) = 0$ true.

$y = 11, - 3$

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 $0$ .

$y = - 3, y = 11$

Step 4

Find Where Undefined/Discontinuous (y^2-22y+121)/(2y^2-16y-66)

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