Pre-Algebra Examples

$f (- \frac{1}{8}) = \frac{x}{x + 1}$

Step 1

Combine $f$ and $\frac{1}{8}$ .

$- \frac{f}{8} = \frac{x}{x + 1}$

Step 2

Divide each term in $- \frac{f}{8} = \frac{x}{x + 1}$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- \frac{f}{8} = \frac{x}{x + 1}$ by $- 1$ .

$\frac{- \frac{f}{8}}{- 1} = \frac{\frac{x}{x + 1}}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{f}{8}}{1} = \frac{\frac{x}{x + 1}}{- 1}$

Step 2.2.2

Divide $\frac{f}{8}$ by $1$ .

$\frac{f}{8} = \frac{\frac{x}{x + 1}}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative one from the denominator of $\frac{\frac{x}{x + 1}}{- 1}$ .

$\frac{f}{8} = - 1 \cdot \frac{x}{x + 1}$

Step 2.3.2

Rewrite $- 1 \cdot \frac{x}{x + 1}$ as $- \frac{x}{x + 1}$ .

$\frac{f}{8} = - \frac{x}{x + 1}$

Step 3

Multiply both sides of the equation by $8$ .

$8 \frac{f}{8} = 8 (- \frac{x}{x + 1})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $8$ .

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Step 4.1.1.1

Cancel the common factor.

$8 \frac{f}{8} = 8 (- \frac{x}{x + 1})$

Step 4.1.1.2

Rewrite the expression.

$f = 8 (- \frac{x}{x + 1})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $8 (- \frac{x}{x + 1})$ .

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Step 4.2.1.1

Multiply $8 (- \frac{x}{x + 1})$ .

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Step 4.2.1.1.1

Multiply $- 1$ by $8$ .

$f = - 8 \frac{x}{x + 1}$

Step 4.2.1.1.2

Combine $- 8$ and $\frac{x}{x + 1}$ .

$f = \frac{- 8 x}{x + 1}$

Step 4.2.1.2

Move the negative in front of the fraction.

$f = - \frac{8 x}{x + 1}$