Algebra Examples

$1 = \frac{1}{x}$

Step 1

Rewrite the equation as $\frac{1}{x} = 1$ .

$\frac{1}{x} = 1$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$x, 1$

Step 2.2

The LCM of one and any expression is the expression.

$x$

Step 3

Multiply each term in $\frac{1}{x} = 1$ by $x$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{1}{x} = 1$ by $x$ .

$\frac{1}{x} x = 1 x$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1}{x} x = 1 x$

Step 3.2.1.2

Rewrite the expression.

$1 = 1 x$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $x$ by $1$ .

$1 = x$

Step 4

Rewrite the equation as $x = 1$ .

$x = 1$