Find Where Undefined/Discontinuous (-20k^4-26k^3)/(12k^4+8k^3)

$\frac{- 20 k^{4} - 26 k^{3}}{12 k^{4} + 8 k^{3}}$

Step 1

Set the denominator in $\frac{- 20 k^{4} - 26 k^{3}}{12 k^{4} + 8 k^{3}}$ equal to $0$ to find where the expression is undefined.

$12 k^{4} + 8 k^{3} = 0$

Step 2

Solve for $k$ .

Factor $4 k^{3}$ out of $12 k^{4} + 8 k^{3}$ .

Factor $4 k^{3}$ out of $12 k^{4}$ .

$4 k^{3} (3 k) + 8 k^{3} = 0$

Factor $4 k^{3}$ out of $8 k^{3}$ .

$4 k^{3} (3 k) + 4 k^{3} (2) = 0$

Factor $4 k^{3}$ out of $4 k^{3} (3 k) + 4 k^{3} (2)$ .

$4 k^{3} (3 k + 2) = 0$

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

$k^{3} = 0$

$3 k + 2 = 0$

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

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

$k^{3} = 0$

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

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

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

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

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

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

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

$k = 0$

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

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

$3 k + 2 = 0$

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

Subtract $2$ from both sides of the equation.

$3 k = - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $k$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The final solution is all the values that make $4 k^{3} (3 k + 2) = 0$ true.

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

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 $0$ .

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

Step 4

Find Where Undefined/Discontinuous (-20k^4-26k^3)/(12k^4+8k^3)

Related Questions

Support LCMGCF.com by disabling your adblocker.