Simplify 1/(x-y)+2/(y-x)

$\frac{1}{x - y} + \frac{2}{y - x}$

Step 1

Factor $- 1$ out of $y$ .

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

Step 2

Factor $- 1$ out of $- x$ .

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

Step 3

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

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

Step 4

Simplify the expression.

Move a negative from the denominator of $\frac{2}{- 1 (- y + x)}$ to the numerator.

$\frac{1}{x - y} + \frac{- 1 \cdot 2}{- y + x}$

Reorder terms.

$\frac{1}{x - y} + \frac{- 1 \cdot 2}{x - y}$

Step 5

Combine the numerators over the common denominator.

$\frac{1 - 1 \cdot 2}{x - y}$

Step 6

Simplify the numerator.

Multiply $- 1$ by $2$ .

$\frac{1 - 2}{x - y}$

Subtract $2$ from $1$ .

$\frac{- 1}{x - y}$

Step 7

Move the negative in front of the fraction.

$- \frac{1}{x - y}$