Question

Thực hiện phép tính A=(x²+y²-xy)/(x²-y²):(x³+y³)/(x²+y²-2xy)

Answer 1

\(A=\dfrac{x^2+y^2-xy}{x^2-y^2}:\dfrac{x^3+y^3}{x^2+y^2-2xy}\)

\(=\dfrac{x^2+y^2-xy}{\left(x-y\right)\left(x+y\right)}\cdot\dfrac{\left(x-y\right)^2}{\left(x+y\right)\left(x^2-xy+y^2\right)}\)

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