Algebra Examples

$\frac{6 x^{3}}{15 x^{4} - 60 x^{3}}$

Step 1

Set the denominator in $\frac{6 x^{3}}{15 x^{4} - 60 x^{3}}$ equal to $0$ to find where the expression is undefined.

$15 x^{4} - 60 x^{3} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Factor $15 x^{3}$ out of $15 x^{4} - 60 x^{3}$ .

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Step 2.1.1

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

$15 x^{3} (x) - 60 x^{3} = 0$

Step 2.1.2

Factor $15 x^{3}$ out of $- 60 x^{3}$ .

$15 x^{3} (x) + 15 x^{3} (- 4) = 0$

Step 2.1.3

Factor $15 x^{3}$ out of $15 x^{3} (x) + 15 x^{3} (- 4)$ .

$15 x^{3} (x - 4) = 0$

Step 2.2

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

$x^{3} = 0$

$x - 4 = 0$

Step 2.3

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

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Step 2.3.1

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

$x^{3} = 0$

Step 2.3.2

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

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Step 2.3.2.1

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

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

Step 2.3.2.2

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

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Step 2.3.2.2.1

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

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

Step 2.3.2.2.2

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

$x = 0$

Step 2.4

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 2.4.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.5

The final solution is all the values that make $15 x^{3} (x - 4) = 0$ true.

$x = 0, 4$

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 $0$ .

$x = 0, x = 4$

Step 4