Find Where Undefined/Discontinuous (-15k^2)/(15k^3+45k^2)

$\frac{- 15 k^{2}}{15 k^{3} + 45 k^{2}}$

Step 1

Set the denominator in $\frac{- 15 k^{2}}{15 k^{3} + 45 k^{2}}$ equal to $0$ to find where the expression is undefined.

$15 k^{3} + 45 k^{2} = 0$

Step 2

Solve for $k$ .

Factor $15 k^{2}$ out of $15 k^{3} + 45 k^{2}$ .

Factor $15 k^{2}$ out of $15 k^{3}$ .

$15 k^{2} (k) + 45 k^{2} = 0$

Factor $15 k^{2}$ out of $45 k^{2}$ .

$15 k^{2} (k) + 15 k^{2} (3) = 0$

Factor $15 k^{2}$ out of $15 k^{2} (k) + 15 k^{2} (3)$ .

$15 k^{2} (k + 3) = 0$

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

$k^{2} = 0$

$k + 3 = 0$

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

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

$k^{2} = 0$

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

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

$k = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

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

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

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

$k = \pm 0$

Plus or minus $0$ is $0$ .

$k = 0$

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

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

$k + 3 = 0$

Subtract $3$ from both sides of the equation.

$k = - 3$

The final solution is all the values that make $15 k^{2} (k + 3) = 0$ true.

$k = 0, - 3$

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 $0$ .

$k = - 3, k = 0$

Step 4

Find Where Undefined/Discontinuous (-15k^2)/(15k^3+45k^2)

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