Basic Math Examples

$\frac{7}{y - 8} - \frac{6}{8 - y}$

Step 1

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{7}{y - 8} - \frac{6}{- 1 (- 8) - y}$

Step 2

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

$\frac{7}{y - 8} - \frac{6}{- 1 (- 8) - (y)}$

Step 3

Factor $- 1$ out of $- 1 (- 8) - (y)$ .

$\frac{7}{y - 8} - \frac{6}{- 1 (- 8 + y)}$

Step 4

Reorder terms.

$\frac{7}{y - 8} - \frac{6}{- 1 (y - 8)}$

Step 5

To write $\frac{7}{y - 8}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{7}{y - 8} \cdot \frac{- 1}{- 1} - \frac{6}{- 1 (y - 8)}$

Step 6

Write each expression with a common denominator of $(y - 8) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{7}{y - 8}$ by $\frac{- 1}{- 1}$ .

$\frac{7 \cdot - 1}{(y - 8) \cdot - 1} - \frac{6}{- 1 (y - 8)}$

Step 6.2

Reorder the factors of $(y - 8) \cdot - 1$ .

$\frac{7 \cdot - 1}{- (y - 8)} - \frac{6}{- 1 (y - 8)}$

Step 7

Combine the numerators over the common denominator.

$\frac{7 \cdot - 1 - 6}{- (y - 8)}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $7$ by $- 1$ .

$\frac{- 7 - 6}{- (y - 8)}$

Step 8.2

Subtract $6$ from $- 7$ .

$\frac{- 13}{- (y - 8)}$

Step 9

Dividing two negative values results in a positive value.

$\frac{13}{y - 8}$