a: \(\dfrac{3}{6x^2yz}=\dfrac{1}{2x^2yz}=\dfrac{y^2}{2x^2y^3z}=\dfrac{2y^2}{4x^2y^3z}\)
\(\dfrac{5}{4xy^3}=\dfrac{5xz}{4x^2y^3z}\)
b: \(\dfrac{3}{x^2-5x}=\dfrac{3}{x\left(x-5\right)}=\dfrac{6}{2x\left(x-5\right)}\)
\(\dfrac{5}{2x-10}=\dfrac{5x}{2x\left(x-5\right)}\)
c: \(\dfrac{5}{2x+6}=\dfrac{5}{2\left(x+3\right)}=\dfrac{5\left(x-3\right)}{2\left(x+3\right)\left(x-3\right)}\)
\(\dfrac{3}{x^2-9}=\dfrac{6}{2\left(x+3\right)\left(x-3\right)}\)
d: \(\dfrac{2x}{x^2-8x+16}=\dfrac{2x}{\left(x-4\right)^2}=\dfrac{6x^2}{3x\left(x-4\right)^2}\)
\(\dfrac{x}{3x^2-12x}=\dfrac{x\left(x-4\right)}{3x\left(x-4\right)^2}\)