\(a,=\dfrac{\left(x-3y\right)\left(x+3y\right)3}{xz\left(x-3y\right)}=\dfrac{3\left(x+3y\right)}{xz}\\ b,=\dfrac{x+y}{\left(x-y\right)^2}\cdot\dfrac{2\left(x-y\right)}{\left(x+y\right)^2}=\dfrac{2}{\left(x-y\right)\left(x+y\right)}\\ c,=\dfrac{9\left(x-y\right)}{\left(x+y\right)^2}\cdot\dfrac{4\left(x+y\right)\left(x^2-xy+y^2\right)}{3\left(x-y\right)}=\dfrac{12\left(x^2-xy+y^2\right)}{x+y}\\ d,=\dfrac{x+y}{y\left(x-y\right)}\cdot\dfrac{x^2+xy-x^2-y^2}{x+y}=\dfrac{y\left(x-y\right)}{y\left(x-y\right)}=1\\ e,=\dfrac{\left(x-5\right)\left(x+5\right)}{x^2+1}\cdot\dfrac{5x^2-26x+5+5x^2+26x+5}{x\left(x-5\right)\left(x+5\right)}\\ =\dfrac{10\left(x^2+1\right)}{x\left(x^2+1\right)}=\dfrac{10}{x}\)
\(f,=\dfrac{\left(x+5\right)\left(x-2\right)}{\left(x+4\right)\left(x-3\right)}\cdot\dfrac{\left(x-3\right)\left(x-4\right)}{\left(x+1\right)\left(x+5\right)}=\dfrac{\left(x-4\right)\left(x-2\right)}{\left(x+1\right)\left(x+4\right)}\)
