Find Where Undefined/Discontinuous (2x^3-3x^2)/(10x^4-15x^3)

$\frac{2 x^{3} - 3 x^{2}}{10 x^{4} - 15 x^{3}}$

Step 1

Set the denominator in $\frac{2 x^{3} - 3 x^{2}}{10 x^{4} - 15 x^{3}}$ equal to $0$ to find where the expression is undefined.

$10 x^{4} - 15 x^{3} = 0$

Step 2

Solve for $x$ .

Factor $5 x^{3}$ out of $10 x^{4} - 15 x^{3}$ .

Factor $5 x^{3}$ out of $10 x^{4}$ .

$5 x^{3} (2 x) - 15 x^{3} = 0$

Factor $5 x^{3}$ out of $- 15 x^{3}$ .

$5 x^{3} (2 x) + 5 x^{3} (- 3) = 0$

Factor $5 x^{3}$ out of $5 x^{3} (2 x) + 5 x^{3} (- 3)$ .

$5 x^{3} (2 x - 3) = 0$

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

$x^{3} = 0$

$2 x - 3 = 0$

Set $x^{3}$ equal to $0$ and solve for $x$ .

Set $x^{3}$ equal to $0$ .

$x^{3} = 0$

Solve $x^{3} = 0$ for $x$ .

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

$x = \sqrt[3]{0}$

Simplify $\sqrt[3]{0}$ .

Rewrite $0$ as $0^{3}$ .

$x = \sqrt[3]{0^{3}}$

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

$x = 0$

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 $x$ .

Add $3$ to 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 $1$ .

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

The final solution is all the values that make $5 x^{3} (2 x - 3) = 0$ true.

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

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 $0$ .

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

Step 4

Find Where Undefined/Discontinuous (2x^3-3x^2)/(10x^4-15x^3)

Related Questions

Support LCMGCF.com by disabling your adblocker.