Find Where Undefined/Discontinuous (5x^3)/(4x+12)*(x^3-9x)/(2x^3+3x^2)

$\frac{5 x^{3}}{4 x + 12} \cdot \frac{x^{3} - 9 x}{2 x^{3} + 3 x^{2}}$

Step 1

Set the denominator in $\frac{5 x^{3}}{4 x + 12}$ equal to $0$ to find where the expression is undefined.

$4 x + 12 = 0$

Step 2

Solve for $x$ .

Subtract $12$ from both sides of the equation.

$4 x = - 12$

Divide each term in $4 x = - 12$ by $4$ and simplify.

Divide each term in $4 x = - 12$ by $4$ .

$\frac{4 x}{4} = \frac{- 12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 12}{4}$

Divide $x$ by $1$ .

$x = \frac{- 12}{4}$

Simplify the right side.

Divide $- 12$ by $4$ .

$x = - 3$

Step 3

Set the denominator in $\frac{x^{3} - 9 x}{2 x^{3} + 3 x^{2}}$ equal to $0$ to find where the expression is undefined.

$2 x^{3} + 3 x^{2} = 0$

Step 4

Solve for $x$ .

Factor $x^{2}$ out of $2 x^{3} + 3 x^{2}$ .

Factor $x^{2}$ out of $2 x^{3}$ .

$x^{2} (2 x) + 3 x^{2} = 0$

Factor $x^{2}$ out of $3 x^{2}$ .

$x^{2} (2 x) + x^{2} \cdot 3 = 0$

Factor $x^{2}$ out of $x^{2} (2 x) + x^{2} \cdot 3$ .

$x^{2} (2 x + 3) = 0$

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

$x^{2} = 0$

$2 x + 3 = 0$

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

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

$x^{2} = 0$

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

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

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

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

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

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

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Set $2 x + 3$ equal to $0$ and solve for $x$ .

Set $2 x + 3$ equal to $0$ .

$2 x + 3 = 0$

Solve $2 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

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

$x = 0, - \frac{3}{2}$

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 $0$ .

$x = - 3, x = - \frac{3}{2}, x = 0$

Step 6

Find Where Undefined/Discontinuous (5x^3)/(4x+12)*(x^3-9x)/(2x^3+3x^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.