Finite Math Examples

$x - \frac{25}{x} = 0$

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 $x - \frac{25}{x} = 0$ by $x$ to eliminate the fractions.

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Step 2.1

Multiply each term in $x - \frac{25}{x} = 0$ by $x$ .

$x \cdot x - \frac{25}{x} x = 0 x$

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 $x$ by $x$ .

$x^{2} - \frac{25}{x} x = 0 x$

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 $- \frac{25}{x}$ into the numerator.

$x^{2} + \frac{- 25}{x} x = 0 x$

Step 2.2.1.2.2

Cancel the common factor.

$x^{2} + \frac{- 25}{x} x = 0 x$

Step 2.2.1.2.3

Rewrite the expression.

$x^{2} - 25 = 0 x$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $0$ by $x$ .

$x^{2} - 25 = 0$

Step 3

Solve the equation.

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Step 3.1

Add $25$ to both sides of the equation.

$x^{2} = 25$

Step 3.2

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

$x = \pm \sqrt{25}$

Step 3.3

Simplify $\pm \sqrt{25}$ .

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Step 3.3.1

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2}}$

Step 3.3.2

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

$x = \pm 5$

Step 3.4

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

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Step 3.4.1

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

$x = 5$

Step 3.4.2

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

$x = - 5$

Step 3.4.3

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

$x = 5, - 5$