Finite Math Examples

$\frac{12}{a - 1} - \frac{12}{1 - a}$

Step 1

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

$\frac{12}{a - 1} - \frac{12}{- 1 (- 1) - a}$

Step 2

Factor $- 1$ out of $- a$ .

$\frac{12}{a - 1} - \frac{12}{- 1 (- 1) - (a)}$

Step 3

Factor $- 1$ out of $- 1 (- 1) - (a)$ .

$\frac{12}{a - 1} - \frac{12}{- 1 (- 1 + a)}$

Step 4

Reorder terms.

$\frac{12}{a - 1} - \frac{12}{- 1 (a - 1)}$

Step 5

To write $\frac{12}{a - 1}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{12}{a - 1} \cdot \frac{- 1}{- 1} - \frac{12}{- 1 (a - 1)}$

Step 6

Write each expression with a common denominator of $(a - 1) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 6.1

Multiply $\frac{12}{a - 1}$ by $\frac{- 1}{- 1}$ .

$\frac{12 \cdot - 1}{(a - 1) \cdot - 1} - \frac{12}{- 1 (a - 1)}$

Step 6.2

Reorder the factors of $(a - 1) \cdot - 1$ .

$\frac{12 \cdot - 1}{- (a - 1)} - \frac{12}{- 1 (a - 1)}$

Step 7

Combine the numerators over the common denominator.

$\frac{12 \cdot - 1 - 12}{- (a - 1)}$

Step 8

Simplify the numerator.

Tap for more steps...

Step 8.1

Multiply $12$ by $- 1$ .

$\frac{- 12 - 12}{- (a - 1)}$

Step 8.2

Subtract $12$ from $- 12$ .

$\frac{- 24}{- (a - 1)}$

Step 9

Dividing two negative values results in a positive value.

$\frac{24}{a - 1}$