Question

rút gọn biểu thức: A\(=\frac{x-y}{xy+y^2}-\frac{3x+y}{x^2-xy}\cdot\frac{y-x}{x+y}\)

Answer 1

A = x-y/x.(x+y) - 3x+y/x.(x-y) . (y-x)/x+y

   = x-y/x.(x+y) + 3x+y/x.(x+y)

   = x-y+3x+y/x.(x+y)

   = 4x/x.(x+y)

    = 4/x+y

Tk mk nha

Answer 2

\(A=\frac{x-y}{xy+y^2}-\frac{3x+y}{x^2-xy}.\frac{y-x}{x+y}\)

    \(=\frac{x-y}{y\left(x+y\right)}-\frac{3x+y}{x\left(x-y\right)}.\frac{-\left(x-y\right)}{x+y}\)

     \(=\frac{x-y}{y\left(x+y\right)}-\frac{-\left(3x+y\right).\left(x-y\right)}{x\left(x-y\right).\left(x-y\right)}\)

      \(=\frac{x-y}{y\left(x+y\right)}-\frac{-\left(3x+y\right)}{x\left(x-y\right)}\)

       \(=\frac{x\left(x-y\right)^2}{xy\left(x+y\right)\left(x-y\right)}+\frac{y\left(3x+y\right)\left(x+y\right)}{xy\left(x+y\right)\left(x-y\right)}\)

\(=\frac{x\left(x^2-2xy+y^2\right)+y\left(3x^2+4xy+y^2\right)}{xy\left(x^2-y^2\right)}\)

  \(=\frac{x^4-2x^2y+xy^2+3x^2y+4xy^2+y^3}{xy\left(x^2-y^2\right)}\)

\(=\frac{x^4+x^2y+5xy^2+y^3}{xy\left(x^2-y^2\right)}=\frac{x^2\left(x^2+y\right)+y^2\left(5x+y\right)}{xy\left(x^2-y^2\right)}\)