Basic Math Examples

$\frac{2}{7 - y} - \frac{2}{y - 7}$

Step 1

Factor $- 1$ out of $y$ .

$\frac{2}{7 - y} - \frac{2}{- 1 (- y) - 7}$

Step 2

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{2}{7 - y} - \frac{2}{- 1 (- y) - 1 (7)}$

Step 3

Factor $- 1$ out of $- 1 (- y) - 1 (7)$ .

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

Step 4

Reorder terms.

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

Step 5

To write $\frac{2}{- y + 7}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

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

Step 6

Write each expression with a common denominator of $(- y + 7) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{2}{- y + 7}$ by $\frac{- 1}{- 1}$ .

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

Step 6.2

Reorder the factors of $(- y + 7) \cdot - 1$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Simplify the numerator.

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Step 8.1

Multiply $2$ by $- 1$ .

$\frac{- 2 - 2}{- (- y + 7)}$

Step 8.2

Subtract $2$ from $- 2$ .

$\frac{- 4}{- (- y + 7)}$

Step 9

Dividing two negative values results in a positive value.

$\frac{4}{- y + 7}$

Step 10

Factor $- 1$ out of $- y$ .

$\frac{4}{- (y) + 7}$

Step 11

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{4}{- (y) - 1 (- 7)}$

Step 12

Factor $- 1$ out of $- (y) - 1 (- 7)$ .

$\frac{4}{- (y - 7)}$

Step 13

Rewrite negatives.

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Step 13.1

Rewrite $- (y - 7)$ as $- 1 (y - 7)$ .

$\frac{4}{- 1 (y - 7)}$

Step 13.2

Move the negative in front of the fraction.

$- \frac{4}{y - 7}$