7) \(\dfrac{3y-2x}{x-2y}-\dfrac{x-y}{2y-x}\)
\(=\dfrac{3y-2x}{x-2y}+\dfrac{x-y}{x-2y}\)
\(=\dfrac{3y-2x+x-y}{x-2y}\)
\(=\dfrac{2y-x}{x-2y}\)
\(=-\dfrac{x-2y}{x-2y}\)
\(=-1\)
5) \(x+\dfrac{2y^2}{x+y}-y\)
\(=\dfrac{x\left(x+y\right)}{x+y}+\dfrac{2y^2}{x+y}-\dfrac{y\left(x+y\right)}{x+y}\)
\(=\dfrac{x^2+xy+2y^2-xy-y^2}{x+y}\)
\(=\dfrac{x^2+y^2}{x+y}\)
8) \(\dfrac{4x+2}{4x-4}+\dfrac{3-6x}{6x-6}\)
\(=\dfrac{2\left(2x+1\right)}{2\left(2x-2\right)}+\dfrac{3\left(1-2x\right)}{3\left(2x-2\right)}\)
\(=\dfrac{2x+1}{2x-2}+\dfrac{1-2x}{2x-2}\)
\(=\dfrac{2x+1+1-2x}{2x-2}\)
\(=\dfrac{2}{2x-2}\)
\(=\dfrac{1}{x-1}\)
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