Pre-Algebra Examples

$\frac{1}{a - 3} - \frac{1}{3 - a}$

Step 1

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{1}{a - 3} - \frac{1}{- 1 (- 3) - a}$

Step 2

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

$\frac{1}{a - 3} - \frac{1}{- 1 (- 3) - (a)}$

Step 3

Factor $- 1$ out of $- 1 (- 3) - (a)$ .

$\frac{1}{a - 3} - \frac{1}{- 1 (- 3 + a)}$

Step 4

Reorder terms.

$\frac{1}{a - 3} - \frac{1}{- 1 (a - 3)}$

Step 5

To write $\frac{1}{a - 3}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{1}{a - 3} \cdot \frac{- 1}{- 1} - \frac{1}{- 1 (a - 3)}$

Step 6

Write each expression with a common denominator of $(a - 3) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{1}{a - 3}$ by $\frac{- 1}{- 1}$ .

$\frac{- 1}{(a - 3) \cdot - 1} - \frac{1}{- 1 (a - 3)}$

Step 6.2

Reorder the factors of $(a - 3) \cdot - 1$ .

$\frac{- 1}{- (a - 3)} - \frac{1}{- 1 (a - 3)}$

Step 7

Combine the numerators over the common denominator.

$\frac{- 1 - 1}{- (a - 3)}$

Step 8

Subtract $1$ from $- 1$ .

$\frac{- 2}{- (a - 3)}$

Step 9

Dividing two negative values results in a positive value.

$\frac{2}{a - 3}$