Algebra Examples

$\frac{8 + \frac{1}{x}}{7 - \frac{1}{x}}$

Step 1

Set the denominator in $\frac{1}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

Set the denominator in $\frac{8 + \frac{1}{x}}{7 - \frac{1}{x}}$ equal to $0$ to find where the expression is undefined.

$7 - \frac{1}{x} = 0$

Step 3

Solve for $x$ .

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Step 3.1

Subtract $7$ from both sides of the equation.

$- \frac{1}{x} = - 7$

Step 3.2

Find the LCD of the terms in the equation.

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Step 3.2.1

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

$x, 1$

Step 3.2.2

The LCM of one and any expression is the expression.

$x$

Step 3.3

Multiply each term in $- \frac{1}{x} = - 7$ by $x$ to eliminate the fractions.

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Step 3.3.1

Multiply each term in $- \frac{1}{x} = - 7$ by $x$ .

$- \frac{1}{x} x = - 7 x$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $x$ .

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Step 3.3.2.1.1

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

$\frac{- 1}{x} x = - 7 x$

Step 3.3.2.1.2

Cancel the common factor.

$\frac{- 1}{x} x = - 7 x$

Step 3.3.2.1.3

Rewrite the expression.

$- 1 = - 7 x$

Step 3.4

Solve the equation.

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Step 3.4.1

Rewrite the equation as $- 7 x = - 1$ .

$- 7 x = - 1$

Step 3.4.2

Divide each term in $- 7 x = - 1$ by $- 7$ and simplify.

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Step 3.4.2.1

Divide each term in $- 7 x = - 1$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 1}{- 7}$

Step 3.4.2.2

Simplify the left side.

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Step 3.4.2.2.1

Cancel the common factor of $- 7$ .

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Step 3.4.2.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 1}{- 7}$

Step 3.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 7}$

Step 3.4.2.3

Simplify the right side.

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Step 3.4.2.3.1

Dividing two negative values results in a positive value.

$x = \frac{1}{7}$

Step 4

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = 0, x = \frac{1}{7}$

Step 5