a: \(\dfrac{14xy^5\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}\)
\(=\dfrac{14xy^5\left(2x-3y\right):7xy\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2:7xy\left(2x-3y\right)}\)
\(=\dfrac{2y^4}{3x\left(2x-3y\right)}\)
b: \(\dfrac{8xy\left(3x-1\right)^3}{12x^3\left(1-3x\right)}\)
\(=\dfrac{-8xy\left(3x-1\right)^3}{12x^3\left(3x-1\right)}\)
\(=\dfrac{-4x\left(3x-1\right)\cdot\left(3x-1\right)^2\cdot2y}{4x\left(3x-1\right)\cdot3x^2}\)
\(=\dfrac{-2y\left(3x-1\right)^2}{3x^2}\)
c: \(\dfrac{20x^2-45}{\left(2x+3\right)^2}\)
\(=\dfrac{5\left(4x^2-9\right)}{\left(2x+3\right)^2}\)
\(=\dfrac{5\left(2x-3\right)\left(2x+3\right)}{\left(2x+3\right)^2}=\dfrac{5\left(2x-3\right)}{2x+3}\)
d: \(\dfrac{5x^2-10xy}{2\left(2y-x\right)^3}\)
\(=\dfrac{-5x\left(x-2y\right)}{2\left(x-2y\right)^3}=\dfrac{-5x}{2\left(x-2y\right)^2}\)
e: \(\dfrac{80x^3-125x}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\)
\(=\dfrac{5x\left(16x^2-25\right)}{\left(x-3\right)\left(3-8+4x\right)}\)
\(=\dfrac{5x\left(4x-5\right)\left(4x+5\right)}{\left(x-3\right)\left(4x-5\right)}=\dfrac{5x\left(4x+5\right)}{x-3}\)
f: \(\dfrac{9-\left(x+5\right)^2}{x^2+4x+4}\)
\(=\dfrac{\left(3-x-5\right)\left(3+x+5\right)}{\left(x+2\right)^2}\)
\(=\dfrac{\left(-x-2\right)\left(x+8\right)}{\left(x+2\right)^2}=\dfrac{-\left(x+8\right)}{x+2}\)
g: \(\dfrac{32x-8x^2+2x^3}{x^3+64}\)
\(=\dfrac{2x\left(x^2-4x+16\right)}{\left(x+4\right)\left(x^2-4x+16\right)}=\dfrac{2x}{x+4}\)
h: \(\dfrac{5x^3+5x}{x^4-1}\)
\(=\dfrac{5x\left(x^2+1\right)}{\left(x^2+1\right)\left(x^2-1\right)}\)
\(=\dfrac{5x}{x^2-1}\)
i: \(\dfrac{x^2+5x+6}{x^2+4x+4}\)
\(=\dfrac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)^2}\)
\(=\dfrac{x+3}{x+2}\)
