Basic Math Examples

$\frac{15}{2 - a} - \frac{7}{a - 2}$

Step 1

Factor $- 1$ out of $a$ .

$\frac{15}{2 - a} - \frac{7}{- 1 (- a) - 2}$

Step 2

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{15}{2 - a} - \frac{7}{- 1 (- a) - 1 (2)}$

Step 3

Factor $- 1$ out of $- 1 (- a) - 1 (2)$ .

$\frac{15}{2 - a} - \frac{7}{- 1 (- a + 2)}$

Step 4

Reorder terms.

$\frac{15}{- a + 2} - \frac{7}{- 1 (- a + 2)}$

Step 5

To write $\frac{15}{- a + 2}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{15}{- a + 2} \cdot \frac{- 1}{- 1} - \frac{7}{- 1 (- a + 2)}$

Step 6

Write each expression with a common denominator of $(- a + 2) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{15}{- a + 2}$ by $\frac{- 1}{- 1}$ .

$\frac{15 \cdot - 1}{(- a + 2) \cdot - 1} - \frac{7}{- 1 (- a + 2)}$

Step 6.2

Reorder the factors of $(- a + 2) \cdot - 1$ .

$\frac{15 \cdot - 1}{- (- a + 2)} - \frac{7}{- 1 (- a + 2)}$

Step 7

Combine the numerators over the common denominator.

$\frac{15 \cdot - 1 - 7}{- (- a + 2)}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $15$ by $- 1$ .

$\frac{- 15 - 7}{- (- a + 2)}$

Step 8.2

Subtract $7$ from $- 15$ .

$\frac{- 22}{- (- a + 2)}$

Step 9

Dividing two negative values results in a positive value.

$\frac{22}{- a + 2}$

Step 10

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

$\frac{22}{- (a) + 2}$

Step 11

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{22}{- (a) - 1 (- 2)}$

Step 12

Factor $- 1$ out of $- (a) - 1 (- 2)$ .

$\frac{22}{- (a - 2)}$

Step 13

Rewrite negatives.

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Step 13.1

Rewrite $- (a - 2)$ as $- 1 (a - 2)$ .

$\frac{22}{- 1 (a - 2)}$

Step 13.2

Move the negative in front of the fraction.

$- \frac{22}{a - 2}$