Finite Math Examples

$\frac{\frac{- 8}{x}}{(\frac{- 8}{x}) - 9}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{- 8}{x} \cdot \frac{1}{\frac{- 8}{x} - 9}$

Step 2

Move the negative in front of the fraction.

$- \frac{8}{x} \cdot \frac{1}{\frac{- 8}{x} - 9}$

Step 3

Simplify the denominator.

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Step 3.1

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$- \frac{8}{x} \cdot \frac{1}{\frac{- 8}{x} - 9 \cdot \frac{x}{x}}$

Step 3.2

Combine $- 9$ and $\frac{x}{x}$ .

$- \frac{8}{x} \cdot \frac{1}{\frac{- 8}{x} + \frac{- 9 x}{x}}$

Step 3.3

Combine the numerators over the common denominator.

$- \frac{8}{x} \cdot \frac{1}{\frac{- 8 - 9 x}{x}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- \frac{8}{x} (1 \frac{x}{- 8 - 9 x})$

Step 5

Multiply $\frac{x}{- 8 - 9 x}$ by $1$ .

$- \frac{8}{x} \cdot \frac{x}{- 8 - 9 x}$

Step 6

Cancel the common factor of $x$ .

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Step 6.1

Move the leading negative in $- \frac{8}{x}$ into the numerator.

$\frac{- 8}{x} \cdot \frac{x}{- 8 - 9 x}$

Step 6.2

Cancel the common factor.

$\frac{- 8}{x} \cdot \frac{x}{- 8 - 9 x}$

Step 6.3

Rewrite the expression.

$- 8 \frac{1}{- 8 - 9 x}$

Step 7

Combine $- 8$ and $\frac{1}{- 8 - 9 x}$ .

$\frac{- 8}{- 8 - 9 x}$

Step 8

Move the negative in front of the fraction.

$- \frac{8}{- 8 - 9 x}$

Step 9

Rewrite $- 8$ as $- 1 (8)$ .

$- \frac{8}{- 1 (8) - 9 x}$

Step 10

Factor $- 1$ out of $- 9 x$ .

$- \frac{8}{- 1 (8) - (9 x)}$

Step 11

Factor $- 1$ out of $- 1 (8) - (9 x)$ .

$- \frac{8}{- 1 (8 + 9 x)}$

Step 12

Simplify the expression.

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Step 12.1

Move the negative in front of the fraction.

$- - \frac{8}{8 + 9 x}$

Step 12.2

Multiply $- 1$ by $- 1$ .

$1 \frac{8}{8 + 9 x}$

Step 12.3

Multiply $\frac{8}{8 + 9 x}$ by $1$ .

$\frac{8}{8 + 9 x}$