Find Where Undefined/Discontinuous (3n^4+6n^3)/(6n^4+9n^3)

$\frac{3 n^{4} + 6 n^{3}}{6 n^{4} + 9 n^{3}}$

Step 1

Set the denominator in $\frac{3 n^{4} + 6 n^{3}}{6 n^{4} + 9 n^{3}}$ equal to $0$ to find where the expression is undefined.

$6 n^{4} + 9 n^{3} = 0$

Step 2

Solve for $n$ .

Factor $3 n^{3}$ out of $6 n^{4} + 9 n^{3}$ .

Factor $3 n^{3}$ out of $6 n^{4}$ .

$3 n^{3} (2 n) + 9 n^{3} = 0$

Factor $3 n^{3}$ out of $9 n^{3}$ .

$3 n^{3} (2 n) + 3 n^{3} (3) = 0$

Factor $3 n^{3}$ out of $3 n^{3} (2 n) + 3 n^{3} (3)$ .

$3 n^{3} (2 n + 3) = 0$

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

$n^{3} = 0$

$2 n + 3 = 0$

Set $n^{3}$ equal to $0$ and solve for $n$ .

Set $n^{3}$ equal to $0$ .

$n^{3} = 0$

Solve $n^{3} = 0$ for $n$ .

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

$n = \sqrt[3]{0}$

Simplify $\sqrt[3]{0}$ .

Rewrite $0$ as $0^{3}$ .

$n = \sqrt[3]{0^{3}}$

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

$n = 0$

Set $2 n + 3$ equal to $0$ and solve for $n$ .

Set $2 n + 3$ equal to $0$ .

$2 n + 3 = 0$

Solve $2 n + 3 = 0$ for $n$ .

Subtract $3$ from both sides of the equation.

$2 n = - 3$

Divide each term in $2 n = - 3$ by $2$ and simplify.

Divide each term in $2 n = - 3$ by $2$ .

$\frac{2 n}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} = \frac{- 3}{2}$

Divide $n$ by $1$ .

$n = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$n = - \frac{3}{2}$

The final solution is all the values that make $3 n^{3} (2 n + 3) = 0$ true.

$n = 0, - \frac{3}{2}$

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 $0$ .

$n = - \frac{3}{2}, n = 0$

Step 4

Find Where Undefined/Discontinuous (3n^4+6n^3)/(6n^4+9n^3)

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