Finite Math Examples

$\frac{x - 9}{2 x} \cdot \frac{9 - x}{6 x}$

Step 1

Multiply $\frac{x - 9}{2 x} \cdot \frac{9 - x}{6 x}$ .

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Step 1.1

Multiply $\frac{x - 9}{2 x}$ by $\frac{9 - x}{6 x}$ .

$\frac{(x - 9) (9 - x)}{2 x (6 x)}$

Step 1.2

Factor $- 1$ out of $x$ .

$\frac{(- 1 (- x) - 9) (9 - x)}{2 x (6 x)}$

Step 1.3

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{(- 1 (- x) - 1 (9)) (9 - x)}{2 x (6 x)}$

Step 1.4

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

$\frac{- 1 (- x + 9) (9 - x)}{2 x (6 x)}$

Step 1.5

Reorder terms.

$\frac{- 1 (- x + 9) (- x + 9)}{2 x (6 x)}$

Step 1.6

Raise $- x + 9$ to the power of $1$ .

$\frac{- 1 ({(- x + 9)}^{1} (- x + 9))}{2 x (6 x)}$

Step 1.7

Raise $- x + 9$ to the power of $1$ .

$\frac{- 1 ({(- x + 9)}^{1} {(- x + 9)}^{1})}{2 x (6 x)}$

Step 1.8

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 1 {(- x + 9)}^{1 + 1}}{2 x (6 x)}$

Step 1.9

Add $1$ and $1$ .

$\frac{- 1 {(- x + 9)}^{2}}{2 x (6 x)}$

Step 1.10

Multiply $6$ by $2$ .

$\frac{- 1 {(- x + 9)}^{2}}{12 x \cdot x}$

Step 1.11

Raise $x$ to the power of $1$ .

$\frac{- 1 {(- x + 9)}^{2}}{12 (x^{1} x)}$

Step 1.12

Raise $x$ to the power of $1$ .

$\frac{- 1 {(- x + 9)}^{2}}{12 (x^{1} x^{1})}$

Step 1.13

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 1 {(- x + 9)}^{2}}{12 x^{1 + 1}}$

Step 1.14

Add $1$ and $1$ .

$\frac{- 1 {(- x + 9)}^{2}}{12 x^{2}}$

Step 2

Move the negative in front of the fraction.

$- \frac{{(- x + 9)}^{2}}{12 x^{2}}$