2)
a) \(\dfrac{x^2+6x+9}{x-1}:\dfrac{2\left(x+3\right)^3}{\left(x-1\right)^2}\left(x\ne1;x\ne-3\right)\)
\(=\dfrac{\left(x+3\right)^2}{x-1}\cdot\dfrac{\left(x-1\right)^2}{2\left(x+3\right)^3}\)
\(=\dfrac{\left(x+3\right)^2\left(x-1\right)^2}{\left(x-1\right)\cdot2\left(x+3\right)^3}\)
\(=\dfrac{x-1}{2\left(x+3\right)}\)
\(=\dfrac{x-1}{2x+6}\)
b) \(\dfrac{5x-10}{x^2+2}:\left(2x-4\right)\left(x\ne2\right)\)
\(=\dfrac{5\left(x-2\right)}{x^2+2}\cdot\dfrac{1}{2x-4}\)
\(=\dfrac{5\left(x-2\right)}{x^2+2}\cdot\dfrac{1}{2\left(x-2\right)}\)
\(=\dfrac{5}{2\left(x^2+2\right)}\)
\(=\dfrac{5}{2x^2+4}\)
c) \(\left(x^2-25\right):\dfrac{2x+10}{3x-7}\)
\(=\left(x+5\right)\left(x-5\right)\cdot\dfrac{3x-7}{2\left(x+5\right)}\)
\(=\left(x-5\right)\cdot\dfrac{3x-7}{2}\)
\(=\dfrac{3x^2-7x-15x+35}{2}\)
\(=\dfrac{3x^2-22x+35}{2}\)