Find Where Undefined/Discontinuous (k^3+16k^2+64k)/(5k^2-25k)*(k^2-13k+40)/(7k^4)

$\frac{k^{3} + 16 k^{2} + 64 k}{5 k^{2} - 25 k} \cdot \frac{k^{2} - 13 k + 40}{7 k^{4}}$

Step 1

Set the denominator in $\frac{k^{3} + 16 k^{2} + 64 k}{5 k^{2} - 25 k}$ equal to $0$ to find where the expression is undefined.

$5 k^{2} - 25 k = 0$

Step 2

Solve for $k$ .

Factor $5 k$ out of $5 k^{2} - 25 k$ .

Factor $5 k$ out of $5 k^{2}$ .

$5 k (k) - 25 k = 0$

Factor $5 k$ out of $- 25 k$ .

$5 k (k) + 5 k (- 5) = 0$

Factor $5 k$ out of $5 k (k) + 5 k (- 5)$ .

$5 k (k - 5) = 0$

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

$k = 0$

$k - 5 = 0$

Set $k$ equal to $0$ .

$k = 0$

Set $k - 5$ equal to $0$ and solve for $k$ .

Set $k - 5$ equal to $0$ .

$k - 5 = 0$

Add $5$ to both sides of the equation.

$k = 5$

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

$k = 0, 5$

Step 3

Set the denominator in $\frac{k^{2} - 13 k + 40}{7 k^{4}}$ equal to $0$ to find where the expression is undefined.

$7 k^{4} = 0$

Step 4

Solve for $k$ .

Divide each term in $7 k^{4} = 0$ by $7$ and simplify.

Divide each term in $7 k^{4} = 0$ by $7$ .

$\frac{7 k^{4}}{7} = \frac{0}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 k^{4}}{7} = \frac{0}{7}$

Divide $k^{4}$ by $1$ .

$k^{4} = \frac{0}{7}$

Simplify the right side.

Divide $0$ by $7$ .

$k^{4} = 0$

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

$k = \pm \sqrt[4]{0}$

Simplify $\pm \sqrt[4]{0}$ .

Rewrite $0$ as $0^{4}$ .

$k = \pm \sqrt[4]{0^{4}}$

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

$k = \pm 0$

Plus or minus $0$ is $0$ .

$k = 0$

Step 5

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 $0$ .

$k = 0, k = 5$

Step 6

Find Where Undefined/Discontinuous (k^3+16k^2+64k)/(5k^2-25k)*(k^2-13k+40)/(7k^4)

Related Questions

Support LCMGCF.com by disabling your adblocker.