a) \(A=\dfrac{y^2\left(x-2\right)\left(x+2\right)}{4xy}.\dfrac{x^2y}{xy\left(2-x\right)}=\dfrac{y\left(x+2\right)}{-4}=-4xy-8y\)
b) \(B=\dfrac{\left(x+2\right)^2}{\left(x+1\right)\left(x+2\right)}.\dfrac{\left(x-2\right)\left(x+1\right)}{x-2}=x+2\)
c) \(C=\dfrac{\left(7y+1\right)\left(y+7\right)+\left(7y-1\right)\left(y-7\right)}{y\left(y-7\right)\left(y+7\right)}.\dfrac{\left(y-7\right)\left(y+7\right)}{y^2+1}=\dfrac{14\left(y^2+1\right)}{y\left(y^2+1\right)}=\dfrac{14}{y}\)
d) \(D=\dfrac{3x\left(2x+1\right)+x\left(1-2x\right)}{\left(1-2x\right)\left(1+2x\right)}.\dfrac{\left(1-2x\right)^2}{4\left(x+1\right)}=\dfrac{4x\left(x+1\right)}{1+2x}.\dfrac{1-2x}{4\left(x+1\right)}=\dfrac{-2x^2+x}{1+2x}\)
