Find Where Undefined/Discontinuous (20n^3+15n^2)/(20n^2+10n)

$\frac{20 n^{3} + 15 n^{2}}{20 n^{2} + 10 n}$

Step 1

Set the denominator in $\frac{20 n^{3} + 15 n^{2}}{20 n^{2} + 10 n}$ equal to $0$ to find where the expression is undefined.

$20 n^{2} + 10 n = 0$

Step 2

Solve for $n$ .

Factor $10 n$ out of $20 n^{2} + 10 n$ .

Factor $10 n$ out of $20 n^{2}$ .

$10 n (2 n) + 10 n = 0$

Factor $10 n$ out of $10 n$ .

$10 n (2 n) + 10 n (1) = 0$

Factor $10 n$ out of $10 n (2 n) + 10 n (1)$ .

$10 n (2 n + 1) = 0$

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

$n = 0$

$2 n + 1 = 0$

Set $n$ equal to $0$ .

$n = 0$

Set $2 n + 1$ equal to $0$ and solve for $n$ .

Set $2 n + 1$ equal to $0$ .

$2 n + 1 = 0$

Solve $2 n + 1 = 0$ for $n$ .

Subtract $1$ from both sides of the equation.

$2 n = - 1$

Divide each term in $2 n = - 1$ by $2$ and simplify.

Divide each term in $2 n = - 1$ by $2$ .

$\frac{2 n}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} = \frac{- 1}{2}$

Divide $n$ by $1$ .

$n = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$n = - \frac{1}{2}$

The final solution is all the values that make $10 n (2 n + 1) = 0$ true.

$n = 0, - \frac{1}{2}$

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 $0$ .

$n = - \frac{1}{2}, n = 0$

Step 4

Find Where Undefined/Discontinuous (20n^3+15n^2)/(20n^2+10n)

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