Find Where Undefined/Discontinuous (-15/(2k^5))÷(5/(6k^5))

$\frac{- 15}{2 k^{5}} \div \frac{5}{6 k^{5}}$

Step 1

Set the denominator in $\frac{- 15}{2 k^{5}}$ equal to $0$ to find where the expression is undefined.

$2 k^{5} = 0$

Step 2

Solve for $k$ .

Divide each term in $2 k^{5} = 0$ by $2$ and simplify.

Divide each term in $2 k^{5} = 0$ by $2$ .

$\frac{2 k^{5}}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 k^{5}}{2} = \frac{0}{2}$

Divide $k^{5}$ by $1$ .

$k^{5} = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$k^{5} = 0$

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

$k = \sqrt[5]{0}$

Simplify $\sqrt[5]{0}$ .

Rewrite $0$ as $0^{5}$ .

$k = \sqrt[5]{0^{5}}$

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

$k = 0$

Step 3

Set the denominator in $\frac{5}{6 k^{5}}$ equal to $0$ to find where the expression is undefined.

$6 k^{5} = 0$

Step 4

Solve for $k$ .

Divide each term in $6 k^{5} = 0$ by $6$ and simplify.

Divide each term in $6 k^{5} = 0$ by $6$ .

$\frac{6 k^{5}}{6} = \frac{0}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 k^{5}}{6} = \frac{0}{6}$

Divide $k^{5}$ by $1$ .

$k^{5} = \frac{0}{6}$

Simplify the right side.

Divide $0$ by $6$ .

$k^{5} = 0$

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

$k = \sqrt[5]{0}$

Simplify $\sqrt[5]{0}$ .

Rewrite $0$ as $0^{5}$ .

$k = \sqrt[5]{0^{5}}$

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

$k = 0$

Step 5

Set the denominator in $\frac{\frac{- 15}{2 k^{5}}}{\frac{5}{6 k^{5}}}$ equal to $0$ to find where the expression is undefined.

$\frac{5}{6 k^{5}} = 0$

Step 6

Solve for $k$ .

Set the numerator equal to zero.

$5 = 0$

Since $5 \neq 0$ , there are no solutions.

No solution

Step 7

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 $0$ .

$k = 0$

Step 8

Find Where Undefined/Discontinuous (-15/(2k^5))÷(5/(6k^5))

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