1: \(\frac{-12x^3y^2}{8x^2y^3}=\frac{-4x^2y^2\cdot3x}{4x^2y^2\cdot2y}=\frac{-3x}{2y}\)
2: \(\frac{15xy^5}{20x^4y^3}=\frac{5xy^3\cdot3y^2}{5xy^3\cdot4x^3}=\frac{3y^2}{4x^3}\)
3: \(\frac{18xy^3\left(2x+1\right)^2}{24x^4\left(2x+1\right)^3}=\frac{6x\left(2x+1\right)^2\cdot3y^3}{6x\left(2x+1\right)^2\cdot4x^3}=\frac{3y^3}{4x^3}\)
4: \(\frac{-9x^4y\left(x-y\right)^3}{12\left(x-y\right)\cdot x^3y^2}=\frac{-3x^3y\left(x-y\right)\cdot3x\left(x-y\right)^2}{3x^3y\left(x-y\right)\cdot4y}=\frac{-3x\left(x-y\right)^2}{4y}\)
5: \(\frac{4+8y}{13y+26y^2}=\frac{4\left(2y+1\right)}{13y\left(2y+1\right)}=\frac{4}{13y}\)
6: \(\frac{x-5}{5x^3-25x^2}=\frac{x-5}{5x^2\cdot\left(x-5\right)}=\frac{1}{5x^2}\)
7: \(\frac{1-x}{x^2y-xy}=\frac{-\left(x-1\right)}{xy\left(x-1\right)}=\frac{-1}{xy}\)
9: \(\frac{x^3-6x_{}^2+9x}{x^2-9}=\frac{x\left(x^2-6x+9\right)}{\left(x-3\right)\left(x+3\right)}=\frac{x\left(x-3\right)^2}{\left(x-3\right)\left(x+3\right)}=\frac{x\left(x-3\right)}{x+3}\)
10: \(\frac{4x^2-4x+1}{6xy-3y}=\frac{\left.\left(2x-1\right)^2\right.}{3y\left(2x-1\right)}=\frac{2x-1}{3y}\)
11: \(\frac{x^3-x}{x^3+2x^2+x}=\frac{x\left(x^2-1\right)}{x\left(x^2+2x+1\right)}=\frac{\left(x-1\right)\left(x+1\right)}{\left(x+1\right)^2}=\frac{x-1}{x+1}\)
12: \(\frac{x^2-9y^2}{x^2-6xy+9y^2}=\frac{\left(x-3y\right)\left(x+3y\right)}{\left(x-3y\right)^2}=\frac{x+3y}{x-3y}\)
13: \(\frac{3x^3-27x}{-6x^2+18x}=\frac{3x\left(x^2-9\right)}{-6x\left(x-3\right)}=\frac{-1}{2}\cdot\frac{\left(x-3\right)\left(x+3\right)}{x-3}=\frac{-x-3}{2}\)
14: \(\frac{x^2-4x+4}{2x_{}^2-4x}=\frac{\left(x-2\right)^2}{2x\left(x-2\right)}=\frac{x-2}{2x}\)
