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5A:
a: ĐKXĐ: \(x\ne\pm y\)
\(\dfrac{2}{x+y}+\dfrac{1}{x-y}+\dfrac{-3x}{x^2-y^2}\)
\(=\dfrac{2}{x+y}+\dfrac{1}{x-y}-\dfrac{3x}{\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{2\left(x-y\right)+x+y-3x}{\left(x+y\right)\left(x-y\right)}\)
\(=\dfrac{2x-2y-2x+y}{\left(x+y\right)\left(x-y\right)}=-\dfrac{y}{\left(x+y\right)\left(x-y\right)}\)
b: ĐKXĐ: x<>-y
\(x+y+\dfrac{x^2+y^2}{x+y}\)
\(=\dfrac{\left(x+y\right)^2+x^2+y^2}{x+y}\)
\(=\dfrac{x^2+2xy+y^2+x^2+y^2}{x+y}=\dfrac{2x^2+2xy+2y^2}{x+y}\)
5B:
a: ĐKXĐ: \(\left\{{}\begin{matrix}x\ne0\\y\ne0\end{matrix}\right.\)
\(\dfrac{5x^2-y^2}{xy}-\dfrac{3x-2y}{y}\)
\(=\dfrac{5x^2-y^2-x\left(3x-2y\right)}{xy}\)
\(=\dfrac{5x^2-y^2-3x^2+2xy}{xy}\)
\(=\dfrac{2x^2+2xy-y^2}{xy}\)
b: ĐKXĐ: \(\left\{{}\begin{matrix}x\ne0\\y\ne0\\x\ne\pm2y\end{matrix}\right.\)
\(\dfrac{2x}{x^2+2xy}+\dfrac{y}{xy-2y^2}+\dfrac{4}{x^2-4y^2}\)
\(=\dfrac{2x}{x\left(x+2y\right)}+\dfrac{y}{y\left(x-2y\right)}+\dfrac{4}{\left(x-2y\right)\cdot\left(x+2y\right)}\)
\(=\dfrac{2}{x+2y}+\dfrac{1}{x-2y}+\dfrac{4}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\dfrac{2x-4y+x+2y+4}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{3x-2y+4}{\left(x-2y\right)\left(x+2y\right)}\)
