Find Where Undefined/Discontinuous (a+4)/(a^2-a-72)

$\frac{a + 4}{a^{2} - a - 72}$

Step 1

Set the denominator in $\frac{a + 4}{a^{2} - a - 72}$ equal to $0$ to find where the expression is undefined.

$a^{2} - a - 72 = 0$

Step 2

Solve for $a$ .

Factor $a^{2} - a - 72$ 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 $- 72$ and whose sum is $- 1$ .

$- 9, 8$

Write the factored form using these integers.

$(a - 9) (a + 8) = 0$

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

$a - 9 = 0$

$a + 8 = 0$

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

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

$a - 9 = 0$

Add $9$ to both sides of the equation.

$a = 9$

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

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

$a + 8 = 0$

Subtract $8$ from both sides of the equation.

$a = - 8$

The final solution is all the values that make $(a - 9) (a + 8) = 0$ true.

$a = 9, - 8$

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 $0$ .

$a = - 8, a = 9$

Step 4

Find Where Undefined/Discontinuous (a+4)/(a^2-a-72)

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