Finite Math Examples

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

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.

$x, 1$

Step 1.2

The LCM of one and any expression is the expression.

$x$

Step 2

Multiply each term in $\frac{4}{x} = 4 x$ by $x$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{4}{x} = 4 x$ by $x$ .

$\frac{4}{x} x = 4 x \cdot x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4}{x} x = 4 x \cdot x$

Step 2.2.1.2

Rewrite the expression.

$4 = 4 x \cdot x$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.3.1.1

Move $x$ .

$4 = 4 (x \cdot x)$

Step 2.3.1.2

Multiply $x$ by $x$ .

$4 = 4 x^{2}$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $4 x^{2} = 4$ .

$4 x^{2} = 4$

Step 3.2

Divide each term in $4 x^{2} = 4$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 x^{2} = 4$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{4}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{4}{4}$

Step 3.2.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{4}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $4$ by $4$ .

$x^{2} = 1$

Step 3.3

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

$x = \pm \sqrt{1}$

Step 3.4

Any root of $1$ is $1$ .

$x = \pm 1$

Step 3.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.5.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Step 3.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1$

Step 3.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1$

Step 4