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

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

Multiply the numerator by the reciprocal of the denominator.

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

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

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

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

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

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

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

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

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

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

Reorder the factors of $(x - y) (x + y)$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Add $2 x$ and $x$ .

$\frac{3 x + 2 y - y}{(x + y) (x - y)} (x - y)$

Subtract $y$ from $2 y$ .

$\frac{3 x + y}{(x + y) (x - y)} (x - y)$

Cancel the common factor of $x - y$ .

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

$\frac{3 x + y}{(x - y) (x + y)} (x - y)$

Cancel the common factor.

$\frac{3 x + y}{(x - y) (x + y)} (x - y)$

Rewrite the expression.

$\frac{3 x + y}{x + y}$