Question

\(\frac{x-y}{x+y}+\frac{x+y}{x-y}+\frac{4y^2}{y^2-x^2}\)

giúp mình nha

 

Answer 1

\(\frac{x-y}{x+y}+\frac{x+y}{x-y}+\frac{4y^2}{y^2-x^2}\)

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

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

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

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

\(=2\)