Basic Math Examples

$\frac{1}{y - 5} - \frac{6}{5 - y}$

Step 1

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{1}{y - 5} - \frac{6}{- 1 (- 5) - y}$

Step 2

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

$\frac{1}{y - 5} - \frac{6}{- 1 (- 5) - (y)}$

Step 3

Factor $- 1$ out of $- 1 (- 5) - (y)$ .

$\frac{1}{y - 5} - \frac{6}{- 1 (- 5 + y)}$

Step 4

Reorder terms.

$\frac{1}{y - 5} - \frac{6}{- 1 (y - 5)}$

Step 5

To write $\frac{1}{y - 5}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{1}{y - 5} \cdot \frac{- 1}{- 1} - \frac{6}{- 1 (y - 5)}$

Step 6

Write each expression with a common denominator of $(y - 5) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{1}{y - 5}$ by $\frac{- 1}{- 1}$ .

$\frac{- 1}{(y - 5) \cdot - 1} - \frac{6}{- 1 (y - 5)}$

Step 6.2

Reorder the factors of $(y - 5) \cdot - 1$ .

$\frac{- 1}{- (y - 5)} - \frac{6}{- 1 (y - 5)}$

Step 7

Combine the numerators over the common denominator.

$\frac{- 1 - 6}{- (y - 5)}$

Step 8

Subtract $6$ from $- 1$ .

$\frac{- 7}{- (y - 5)}$