Find Where Undefined/Discontinuous (6a^2+12a)/(9a^3+18a^2)

$\frac{6 a^{2} + 12 a}{9 a^{3} + 18 a^{2}}$

Step 1

Set the denominator in $\frac{6 a^{2} + 12 a}{9 a^{3} + 18 a^{2}}$ equal to $0$ to find where the expression is undefined.

$9 a^{3} + 18 a^{2} = 0$

Step 2

Solve for $a$ .

Factor $9 a^{2}$ out of $9 a^{3} + 18 a^{2}$ .

Factor $9 a^{2}$ out of $9 a^{3}$ .

$9 a^{2} (a) + 18 a^{2} = 0$

Factor $9 a^{2}$ out of $18 a^{2}$ .

$9 a^{2} (a) + 9 a^{2} (2) = 0$

Factor $9 a^{2}$ out of $9 a^{2} (a) + 9 a^{2} (2)$ .

$9 a^{2} (a + 2) = 0$

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

$a^{2} = 0$

$a + 2 = 0$

Set $a^{2}$ equal to $0$ and solve for $a$ .

Set $a^{2}$ equal to $0$ .

$a^{2} = 0$

Solve $a^{2} = 0$ for $a$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$a = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$a = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$a = \pm 0$

Plus or minus $0$ is $0$ .

$a = 0$

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

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

$a + 2 = 0$

Subtract $2$ from both sides of the equation.

$a = - 2$

The final solution is all the values that make $9 a^{2} (a + 2) = 0$ true.

$a = 0, - 2$

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 $0$ .

$a = - 2, a = 0$

Step 4

Find Where Undefined/Discontinuous (6a^2+12a)/(9a^3+18a^2)

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