Simplify the expression (1)/(x-y) − (1)/(x+y) + (2x)/(x2-y2)

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We need to simplify the expression $\frac{1}{x-y} - \frac{1}{x+y} + \frac{2x}{x^2-y^2}$ .
We assume the third term's denominator is $x^2-y^2$ , as this allows for simplification with the other terms.

Combine the first two fractions by finding a common denominator, which is $(x-y)(x+y) = x^2-y^2$ .
$\frac{1}{x-y} - \frac{1}{x+y} = \frac{1 \cdot (x+y)}{(x-y)(x+y)} - \frac{1 \cdot (x-y)}{(x+y)(x-y)}$ $= \frac{x+y - (x-y)}{x^2-y^2} = \frac{x+y-x+y}{x^2-y^2} = \frac{2y}{x^2-y^2}$
Add the result from Step 1 to the third fraction.
$\frac{2y}{x^2-y^2} + \frac{2x}{x^2-y^2} = \frac{2y+2x}{x^2-y^2}$
Factor

Simplify the expression (1)/(x-y) - (1)/(x+y) + (2x)/(x2-y2)

Step-by-step solution

Combine the first two fractions by finding a common denominator, which is $(x-y)(x+y) = x^2-y^2$ .

Add the result from Step 1 to the third fraction.

Factor

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