Bài 17:
a: \(M=\dfrac{x-2y}{3x+6y}:\dfrac{x^2-4y^2}{x^2+4xy+4y^2}\)
\(=\dfrac{x-2y}{3\left(x+2y\right)}\cdot\dfrac{x^2+4xy+4y^2}{x^2-4y^2}\)
\(=\dfrac{x-2y}{3\left(x+2y\right)}\cdot\dfrac{\left(x+2y\right)^2}{\left(x-2y\right)\left(x+2y\right)}\)
\(=\dfrac{1}{3}\)
b: \(N=\left(x-\dfrac{x^2+y^2}{x+y}\right)\left(\dfrac{1}{y}+\dfrac{2}{x-y}\right)\)
\(=\dfrac{x\left(x+y\right)-\left(x^2+y^2\right)}{x+y}\cdot\dfrac{x-y+2y}{y\left(x-y\right)}\)
\(=\dfrac{x^2+xy-x^2-y^2}{x+y}\cdot\dfrac{x+y}{y\left(x-y\right)}\)
\(=\dfrac{xy-y^2}{y\left(x-y\right)}=\dfrac{y\left(x-y\right)}{y\left(x-y\right)}=1\)
c: \(P=\left(\dfrac{x^3+y^3}{x+y}-xy\right):\left(x^2-y^2\right)+\dfrac{2y}{x+y}\)
\(=\dfrac{\left(\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{x+y}-xy\right)}{x^2-y^2}+\dfrac{2y}{x+y}\)
\(=\dfrac{\left(x^2-xy+y^2-xy\right)}{\left(x-y\right)\left(x+y\right)}+\dfrac{2y}{x+y}\)
\(=\dfrac{\left(x-y\right)^2}{\left(x-y\right)\left(x+y\right)}+\dfrac{2y}{x+y}\)
\(=\dfrac{x-y}{x+y}+\dfrac{2y}{x+y}=\dfrac{x-y+2y}{x+y}=1\)
