Find Where Undefined/Discontinuous (y^2+8y+16)/(y^2-5y-36)

$\frac{y^{2} + 8 y + 16}{y^{2} - 5 y - 36}$

Step 1

Set the denominator in $\frac{y^{2} + 8 y + 16}{y^{2} - 5 y - 36}$ equal to $0$ to find where the expression is undefined.

$y^{2} - 5 y - 36 = 0$

Step 2

Solve for $y$ .

Factor $y^{2} - 5 y - 36$ 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 $- 36$ and whose sum is $- 5$ .

$- 9, 4$

Write the factored form using these integers.

$(y - 9) (y + 4) = 0$

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

$y - 9 = 0$

$y + 4 = 0$

Set $y - 9$ equal to $0$ and solve for $y$ .

Set $y - 9$ equal to $0$ .

$y - 9 = 0$

Add $9$ to both sides of the equation.

$y = 9$

Set $y + 4$ equal to $0$ and solve for $y$ .

Set $y + 4$ equal to $0$ .

$y + 4 = 0$

Subtract $4$ from both sides of the equation.

$y = - 4$

The final solution is all the values that make $(y - 9) (y + 4) = 0$ true.

$y = 9, - 4$

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 $0$ .

$y = - 4, y = 9$

Step 4

Find Where Undefined/Discontinuous (y^2+8y+16)/(y^2-5y-36)

Related Questions

Support LCMGCF.com by disabling your adblocker.