Algebra Examples

$x^{2} - \frac{2}{x} = 0$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, x, 1$

Step 1.2

The LCM of one and any expression is the expression.

$x$

Step 2

Multiply each term in $x^{2} - \frac{2}{x} = 0$ by $x$ to eliminate the fractions.

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Step 2.1

Multiply each term in $x^{2} - \frac{2}{x} = 0$ by $x$ .

$x^{2} x - \frac{2}{x} x = 0 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.2.1.1.1

Multiply $x^{2}$ by $x$ .

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Step 2.2.1.1.1.1

Raise $x$ to the power of $1$ .

$x^{2} x^{1} - \frac{2}{x} x = 0 x$

Step 2.2.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 1} - \frac{2}{x} x = 0 x$

Step 2.2.1.1.2

Add $2$ and $1$ .

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

Step 2.2.1.2

Cancel the common factor of $x$ .

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Step 2.2.1.2.1

Move the leading negative in $- \frac{2}{x}$ into the numerator.

$x^{3} + \frac{- 2}{x} x = 0 x$

Step 2.2.1.2.2

Cancel the common factor.

$x^{3} + \frac{- 2}{x} x = 0 x$

Step 2.2.1.2.3

Rewrite the expression.

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $0$ by $x$ .

$x^{3} - 2 = 0$

Step 3

Solve the equation.

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Step 3.1

Add $2$ to both sides of the equation.

$x^{3} = 2$

Step 3.2

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

$x = \sqrt[3]{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[3]{2}$

Decimal Form:

$x = 1.25992104 \dots$