Simplify ((x+y)/(x-y))÷(4/(y-x))

$\frac{x + y}{x - y} \div \frac{4}{y - x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x + y}{x - y} \cdot \frac{y - x}{4}$

Step 2

Multiply $\frac{x + y}{x - y}$ by $\frac{y - x}{4}$ .

$\frac{(x + y) (y - x)}{(x - y) \cdot 4}$

Step 3

Cancel the common factor of $y - x$ and $x - y$ .

Factor $- 1$ out of $y$ .

$\frac{(x + y) (- 1 (- y) - x)}{(x - y) \cdot 4}$

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

$\frac{(x + y) (- 1 (- y) - (x))}{(x - y) \cdot 4}$

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

$\frac{(x + y) (- 1 (- y + x))}{(x - y) \cdot 4}$

Reorder terms.

$\frac{(x + y) (- 1 (x - y))}{(x - y) \cdot 4}$

Cancel the common factor.

$\frac{(x + y) (- 1 (x - y))}{(x - y) \cdot 4}$

Rewrite the expression.

$\frac{(x + y) \cdot (- 1)}{4}$

Step 4

Simplify the expression.

Move $- 1$ to the left of $x + y$ .

$\frac{- 1 \cdot (x + y)}{4}$

Move the negative in front of the fraction.

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