c: \(\dfrac{x^2+2x}{x^2-2x+1}:\dfrac{x^2-4}{x^2-x}\)
\(=\dfrac{x\left(x+2\right)}{\left(x-1\right)^2}:\dfrac{\left(x-2\right)\left(x+2\right)}{x\left(x-1\right)}\)
\(=\dfrac{x\left(x+2\right)}{\left(x-1\right)^2}\cdot\dfrac{x\left(x-1\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2}{\left(x-1\right)\left(x-2\right)}\)
d: \(\dfrac{2x+3y}{2-x}:\dfrac{4x^2+12xy+9y^2}{x^3-8}\)
\(=\dfrac{2x+3y}{-\left(x-2\right)}:\dfrac{\left(2x+3y\right)^2}{\left(x-2\right)\left(x^2+2x+4\right)}\)
\(=\dfrac{-\left(2x+3y\right)}{x-2}\cdot\dfrac{\left(x-2\right)\left(x^2+2x+4\right)}{\left(2x+3y\right)^2}\)
\(=\dfrac{-\left(x^2+2x+4\right)}{2x+3y}\)
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