2:
a: \(\dfrac{3}{5a}\cdot\dfrac{2b}{5}=\dfrac{3\cdot2b}{5a\cdot5}=\dfrac{6b}{25a}\)
b: \(\dfrac{2a}{3}\cdot\dfrac{6}{4b}=\dfrac{2a\cdot6}{3\cdot4b}=\dfrac{12a}{12b}=\dfrac{a}{b}\)
c: \(\dfrac{a^2}{15}\cdot\dfrac{5}{a}=\dfrac{a^2\cdot5}{15\cdot a}=\dfrac{5a^2}{15a}=\dfrac{a}{3}\)
d: \(\dfrac{18}{a^3}\cdot\dfrac{a^2}{30a}\)
\(=\dfrac{18a^2}{a^3\cdot30a}=\dfrac{18}{30}\cdot\dfrac{a^2}{a^4}=\dfrac{3}{5a^2}\)
e: \(\dfrac{x^2-5x}{4y^2}:\dfrac{5x}{2y}\)
\(=\dfrac{x\left(x-5\right)}{4y^2}\cdot\dfrac{2y}{5x}\)
\(=\dfrac{x-5}{5}\cdot\dfrac{2y}{4y^2}=\dfrac{x-5}{5}\cdot\dfrac{1}{2y}=\dfrac{x-5}{10y}\)
f: \(\dfrac{x^2-1}{y}:\dfrac{x+1}{y^2}\)
\(=\dfrac{\left(x-1\right)\left(x+1\right)}{y}\cdot\dfrac{y^2}{x+1}\)
\(=y\left(x-1\right)\)
g: \(\left(x^2-2xy\right):\dfrac{5x-10y}{x}\)
\(=\dfrac{x\left(x-2y\right)\cdot x}{5\left(x-2y\right)}=\dfrac{x^2}{5}\)
h: \(\dfrac{x^2-x}{x-y}:\left(x^2+xy\right)\)
\(=\dfrac{x\left(x-1\right)}{\left(x-y\right)\left(x^2+xy\right)}\)
\(=\dfrac{x\left(x-1\right)}{x\left(x+y\right)\left(x-y\right)}=\dfrac{x-1}{x^2-y^2}\)
