a: \(=\left(\dfrac{2ab}{\left(a-b\right)\left(a+b\right)}+\dfrac{a-b}{2\left(â+b\right)}\right)\cdot\dfrac{2a}{a+b}-\dfrac{b}{a-b}\)
\(=\dfrac{4ab+a^2-2ab+b^2}{2\left(a+b\right)\left(a-b\right)}\cdot\dfrac{2a}{a+b}-\dfrac{b}{a-b}\)
\(=\dfrac{\left(a+b\right)^2\cdot a}{\left(a+b\right)^2\cdot\left(a-b\right)}-\dfrac{b}{a-b}=\dfrac{a}{a-b}-\dfrac{b}{a-b}=1\)
b: \(=\dfrac{x}{x-y}-\dfrac{x\left(x-y\right)\left(x+y\right)}{x^2+y^2}\cdot\dfrac{x\left(x+y\right)-y\left(x-y\right)}{\left(x-y\right)^2\cdot\left(x+y\right)}\)
\(=\dfrac{x}{x-y}-\dfrac{x}{x^2+y^2}\cdot\dfrac{x^2+xy-xy+y^2}{x-y}\)
\(=\dfrac{x}{x-y}-\dfrac{x}{x-y}=0\)
c: \(=\dfrac{-y}{y-3}+\dfrac{y\left(y+3\right)}{2y+3}\cdot\dfrac{y^2+6y+9-y^2}{y\left(y-3\right)\left(y+3\right)}\)
\(=\dfrac{-y}{y-3}+\dfrac{3\left(2y+3\right)}{\left(2y+3\right)\left(y-3\right)}=\dfrac{-y+3}{y-3}=-1\)
d: \(=\left(\dfrac{x}{\left(x-6\right)\left(x+6\right)}-\dfrac{x-6}{x\left(x+6\right)}\right)\cdot\dfrac{x\left(x+6\right)}{2\left(x-3\right)}-\dfrac{x}{x-6}\)
\(=\dfrac{x^2-x^2+12x-36}{x\left(x-6\right)\left(x+6\right)}\cdot\dfrac{x\left(x+6\right)}{2\left(x-3\right)}-\dfrac{x}{x-6}\)
\(=\dfrac{12\left(x-3\right)}{2\left(x-3\right)\left(x-6\right)}-\dfrac{x}{x-6}=\dfrac{6-x}{x-6}=-1\)
