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\frac{x}{x+y}-\left(\frac{y}{x-y}+\frac{x-y}{x-y}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-y}{x-y}.
\frac{x}{x+y}-\frac{y+x-y}{x-y}
Since \frac{y}{x-y} and \frac{x-y}{x-y} have the same denominator, add them by adding their numerators.
\frac{x}{x+y}-\frac{x}{x-y}
Combine like terms in y+x-y.
\frac{x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}-\frac{x\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+y and x-y is \left(x+y\right)\left(x-y\right). Multiply \frac{x}{x+y} times \frac{x-y}{x-y}. Multiply \frac{x}{x-y} times \frac{x+y}{x+y}.
\frac{x\left(x-y\right)-x\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}
Since \frac{x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} and \frac{x\left(x+y\right)}{\left(x+y\right)\left(x-y\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-xy-x^{2}-xy}{\left(x+y\right)\left(x-y\right)}
Do the multiplications in x\left(x-y\right)-x\left(x+y\right).
\frac{-2xy}{\left(x+y\right)\left(x-y\right)}
Combine like terms in x^{2}-xy-x^{2}-xy.
\frac{-2xy}{x^{2}-y^{2}}
Expand \left(x+y\right)\left(x-y\right).
\frac{x}{x+y}-\left(\frac{y}{x-y}+\frac{x-y}{x-y}\right)
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-y}{x-y}.
\frac{x}{x+y}-\frac{y+x-y}{x-y}
Since \frac{y}{x-y} and \frac{x-y}{x-y} have the same denominator, add them by adding their numerators.
\frac{x}{x+y}-\frac{x}{x-y}
Combine like terms in y+x-y.
\frac{x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}-\frac{x\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+y and x-y is \left(x+y\right)\left(x-y\right). Multiply \frac{x}{x+y} times \frac{x-y}{x-y}. Multiply \frac{x}{x-y} times \frac{x+y}{x+y}.
\frac{x\left(x-y\right)-x\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}
Since \frac{x\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} and \frac{x\left(x+y\right)}{\left(x+y\right)\left(x-y\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-xy-x^{2}-xy}{\left(x+y\right)\left(x-y\right)}
Do the multiplications in x\left(x-y\right)-x\left(x+y\right).
\frac{-2xy}{\left(x+y\right)\left(x-y\right)}
Combine like terms in x^{2}-xy-x^{2}-xy.
\frac{-2xy}{x^{2}-y^{2}}
Expand \left(x+y\right)\left(x-y\right).