\(P=\dfrac{x+y-1}{x\left(x+y\right)}+\dfrac{x-y}{2xy}\cdot\dfrac{y\left(x+y\right)+y\left(x-y\right)}{x\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{x+y-1}{x\left(x+y\right)}+\dfrac{xy+y^2+xy-y^2}{2x^2y\left(x+y\right)}\)
\(=\dfrac{x+y-1}{x\left(x+y\right)}+\dfrac{1}{x\left(x+y\right)}=\dfrac{1}{x}\)
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