Find Where Undefined/Discontinuous (q^2+11q+24)/(q^2-5q-24)

$\frac{(q^{2} + 11 q + 24)}{q^{2} - 5 q - 24}$

Step 1

Set the denominator in $\frac{q^{2} + 11 q + 24}{q^{2} - 5 q - 24}$ equal to $0$ to find where the expression is undefined.

$q^{2} - 5 q - 24 = 0$

Step 2

Solve for $q$ .

Factor $q^{2} - 5 q - 24$ 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 $- 24$ and whose sum is $- 5$ .

$- 8, 3$

Write the factored form using these integers.

$(q - 8) (q + 3) = 0$

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

$q - 8 = 0$

$q + 3 = 0$

Set $q - 8$ equal to $0$ and solve for $q$ .

Set $q - 8$ equal to $0$ .

$q - 8 = 0$

Add $8$ to both sides of the equation.

$q = 8$

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

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

$q + 3 = 0$

Subtract $3$ from both sides of the equation.

$q = - 3$

The final solution is all the values that make $(q - 8) (q + 3) = 0$ true.

$q = 8, - 3$

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 $0$ .

$q = - 3, q = 8$

Step 4

Find Where Undefined/Discontinuous (q^2+11q+24)/(q^2-5q-24)

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