Calculus Examples

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

Step 1

Subtract $1$ from both sides of the equation.

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

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 $x$ .

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

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

Move the leading negative in $- \frac{1}{x}$ into the numerator.

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

Step 3.2.1.2

Cancel the common factor.

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

Step 3.2.1.3

Rewrite the expression.

$- 1 = - x$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $- x = - 1$ .

$- x = - 1$

Step 4.2

Divide each term in $- x = - 1$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- x = - 1$ by $- 1$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

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

Step 4.2.2.2

Divide $x$ by $1$ .

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 1$ by $- 1$ .

$x = 1$