Question

[trần thị mai]

Rút gọn biểu thức: 

\(A=\left[\frac{1}{x^2+2xy+y^2}-\frac{1}{x^2-y^2}\right]:\frac{4xy}{y^2-x^2}\)

Giúp nha m.n! thanks!!!

Answer 1

[Thúy Ngân]

Ta có: \(A=\left(\frac{1}{x^2+2xy+y^2}-\frac{1}{x^2-y^2}\right):\frac{4xy}{y^2-x^2}\)

\(=\left[\frac{1}{\left(x+y\right)^2}-\frac{1}{\left(x+y\right)\left(x-y\right)}\right].\frac{\left(y+x\right)\left(y-x\right)}{4xy}\)

\(=\frac{1}{x+y}\left(\frac{1}{x+y}-\frac{1}{x-y}\right).\frac{\left(x+y\right)\left(y-x\right)}{4xy}\)

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

\(=\frac{1}{\left(x+y\right).2x}\)

Kb với mình nha mn!