a: \(=\dfrac{y^2\left(x-2\right)\left(x+2\right)}{4xy}\cdot\dfrac{x^2y}{xy\left(2-x\right)}\)
\(=\dfrac{-y^2\left(x+2\right)\cdot x}{4xy}=\dfrac{-y\left(x+2\right)}{4}\)
b: \(=\left(\dfrac{\left(7y+1\right)\left(y+7\right)+\left(7y-1\right)\left(y-7\right)}{y\left(y-7\right)\left(y+7\right)}\right)\cdot\dfrac{\left(y-7\right)\left(y+7\right)}{y^2+1}\)
\(=\dfrac{7y^2+50y+7+7y^2-50y+7}{y}\cdot\dfrac{1}{y^2+1}=\dfrac{7}{y}\)
c: \(=\dfrac{-6x^2-3x+2x^2-x}{\left(2x+1\right)\left(2x-1\right)}\cdot\dfrac{\left(2x-1\right)^2}{4\left(x+1\right)}\)
\(=\dfrac{-4x^2-4x}{\left(2x+1\right)}\cdot\dfrac{2x-1}{4\left(x+1\right)}=\dfrac{-4x\left(x+1\right)}{4\left(x+1\right)}\cdot\dfrac{2x-1}{2x+1}\)
=-x(2x-1)/(2x+1)
