Find Where Undefined/Discontinuous (5a)/(a^2+4a-12)

$\frac{5 a}{a^{2} + 4 a - 12}$

Step 1

Set the denominator in $\frac{5 a}{a^{2} + 4 a - 12}$ equal to $0$ to find where the expression is undefined.

$a^{2} + 4 a - 12 = 0$

Step 2

Solve for $a$ .

Factor $a^{2} + 4 a - 12$ 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 $- 12$ and whose sum is $4$ .

$- 2, 6$

Write the factored form using these integers.

$(a - 2) (a + 6) = 0$

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

$a - 2 = 0$

$a + 6 = 0$

Set $a - 2$ equal to $0$ and solve for $a$ .

Set $a - 2$ equal to $0$ .

$a - 2 = 0$

Add $2$ to both sides of the equation.

$a = 2$

Set $a + 6$ equal to $0$ and solve for $a$ .

Set $a + 6$ equal to $0$ .

$a + 6 = 0$

Subtract $6$ from both sides of the equation.

$a = - 6$

The final solution is all the values that make $(a - 2) (a + 6) = 0$ true.

$a = 2, - 6$

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 $0$ .

$a = - 6, a = 2$

Step 4

Find Where Undefined/Discontinuous (5a)/(a^2+4a-12)

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