Find the Excluded Values (y+5)/(y^2+4y-32)

$\frac{y + 5}{y^{2} + 4 y - 32}$

Set the denominator in $\frac{y + 5}{y^{2} + 4 y - 32}$ equal to $0$ to find where the expression is undefined.

$y^{2} + 4 y - 32 = 0$

Solve for $y$ .

Factor $y^{2} + 4 y - 32$ 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 $- 32$ and whose sum is $4$ .

$- 4, 8$

Write the factored form using these integers.

$(y - 4) (y + 8) = 0$

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

$y - 4 = 0$

$y + 8 = 0$

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

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

$y - 4 = 0$

Add $4$ to both sides of the equation.

$y = 4$

Set $y + 8$ equal to $0$ and solve for $y$ .

Set $y + 8$ equal to $0$ .

$y + 8 = 0$

Subtract $8$ from both sides of the equation.

$y = - 8$

The final solution is all the values that make $(y - 4) (y + 8) = 0$ true.

$y = 4, - 8$

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 $0$ .

$y = - 8, y = 4$

Find the Excluded Values (y+5)/(y^2+4y-32)

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