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\frac{-4}{\left(x+y\right)^{2}}
Since \frac{-2}{\left(x+y\right)^{2}} and \frac{2}{\left(x+y\right)^{2}} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from -2 to get -4.
\frac{-4}{x^{2}+2xy+y^{2}}
Expand \left(x+y\right)^{2}.
\frac{-4}{\left(x+y\right)^{2}}
Since \frac{-2}{\left(x+y\right)^{2}} and \frac{2}{\left(x+y\right)^{2}} have the same denominator, subtract them by subtracting their numerators. Subtract 2 from -2 to get -4.
\frac{-4}{x^{2}+2xy+y^{2}}
Expand \left(x+y\right)^{2}.