Find Where Undefined/Discontinuous (11k)/(55k^2+22k)

$\frac{11 k}{55 k^{2} + 22 k}$

Step 1

Set the denominator in $\frac{11 k}{55 k^{2} + 22 k}$ equal to $0$ to find where the expression is undefined.

$55 k^{2} + 22 k = 0$

Step 2

Solve for $k$ .

Factor $11 k$ out of $55 k^{2} + 22 k$ .

Factor $11 k$ out of $55 k^{2}$ .

$11 k (5 k) + 22 k = 0$

Factor $11 k$ out of $22 k$ .

$11 k (5 k) + 11 k (2) = 0$

Factor $11 k$ out of $11 k (5 k) + 11 k (2)$ .

$11 k (5 k + 2) = 0$

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

$k = 0$

$5 k + 2 = 0$

Set $k$ equal to $0$ .

$k = 0$

Set $5 k + 2$ equal to $0$ and solve for $k$ .

Set $5 k + 2$ equal to $0$ .

$5 k + 2 = 0$

Solve $5 k + 2 = 0$ for $k$ .

Subtract $2$ from both sides of the equation.

$5 k = - 2$

Divide each term in $5 k = - 2$ by $5$ and simplify.

Divide each term in $5 k = - 2$ by $5$ .

$\frac{5 k}{5} = \frac{- 2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 k}{5} = \frac{- 2}{5}$

Divide $k$ by $1$ .

$k = \frac{- 2}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$k = - \frac{2}{5}$

The final solution is all the values that make $11 k (5 k + 2) = 0$ true.

$k = 0, - \frac{2}{5}$

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 $0$ .

$k = - \frac{2}{5}, k = 0$

Step 4

Find Where Undefined/Discontinuous (11k)/(55k^2+22k)

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