1: \(\dfrac{8xy\left(3x-1\right)^3}{12x^3\left(1-3x\right)}\)
\(=-\dfrac{8}{12}\cdot\dfrac{x}{x^3}\cdot y\cdot\dfrac{\left(3x-1\right)^3}{3x-1}\)
\(=\dfrac{-2y\left(3x-1\right)^2}{3x^2}\)
2: \(\dfrac{14xy^5\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}\)
\(=\dfrac{14}{21}\cdot\dfrac{x}{x^2}\cdot\dfrac{y^5}{y}\cdot\dfrac{2x-3y}{\left(2x-3y\right)^2}\)
\(=\dfrac{2y^4}{3x\left(2x-3y\right)}\)
3: \(\dfrac{20x^2-45}{\left(2x+3\right)^2}\)
\(=\dfrac{5\left(4x^2-9\right)}{\left(2x+3\right)^2}\)
\(=\dfrac{5\left(2x-3\right)\left(2x+3\right)}{\left(2x+3\right)^2}=\dfrac{5\left(2x-3\right)}{2x+3}\)
5: \(\dfrac{48a^3-75a}{3\left(a-2\right)-\left(a-2\right)\left(8-4a\right)}\)
\(=\dfrac{3a\cdot16a^2-3a\cdot25}{\left(a-2\right)\left(3-8+4a\right)}\)
\(=\dfrac{3a\left(16a^2-25\right)}{\left(a-2\right)\left(4a-5\right)}\)
\(=\dfrac{3a\left(4a-5\right)\left(4a+5\right)}{\left(a-2\right)\left(4a-5\right)}=\dfrac{3a\left(4a+5\right)}{a-2}\)