a: \(=\dfrac{30x^2y^2}{7z}\cdot\dfrac{35z^3}{24x^2y}=\dfrac{5}{4}y\cdot5z^2=\dfrac{25yz^2}{4}\)
b: \(=-\dfrac{25x^3y^5}{3x}\cdot\dfrac{1}{15xy^2}=\dfrac{-25x^3y^5}{45x^2y^2}=-\dfrac{5}{9}xy^3\)
c: \(=\dfrac{5\left(x-1\right)}{\left(x+1\right)^2}\cdot\dfrac{3\left(x+1\right)}{20\left(x-1\right)\left(x+1\right)}=\dfrac{3}{4\left(x+1\right)^2}\)
d: \(=\dfrac{x\left(x+y\right)}{5\left(x-y\right)\left(x+y\right)}\cdot\dfrac{3\left(x^2+y^2\right)}{x\left(x-y\right)}=\dfrac{3\left(x^2+y^2\right)}{5}\)
\(\left(-\dfrac{30x^2y^2}{7z}\right):\left(-\dfrac{24x^3y}{35z^2}\right)\)
\(=\dfrac{30x^2y^2}{7x}.\dfrac{35z^2}{24x^3y}\)
\(=\dfrac{1050x^2y^2z^2}{168x^4y}=\dfrac{25yz}{4x^2}\)
