Question

Tìm phân thức Q, biết: \(\dfrac{x-y}{x^3+y^3}.Q=\dfrac{x^2-2xy+y^2}{x^2-xy+y^2}\)

Answer 1

\(\dfrac{x-y}{x^3+y^3}.Q=\dfrac{x^2-2xy+y^2}{x^2-xy+y^2}\)

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

\(\Leftrightarrow Q=\dfrac{x^2-2xy+y^2}{x^2-xy+y^2}.\dfrac{x^3+y^3}{x-y}\)

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

\(\Rightarrow Q=\left(x-y\right)\left(x+y\right)\)

Answer 2

\(\dfrac{x-y}{x^3+y^3}.Q=\dfrac{x^2-2xy+y^2}{x^2-xy+y^2}\\ \Rightarrow Q=\dfrac{x^2-2xy+y^2}{x^2-xy+y^2}:\dfrac{x-y}{x^3+y^3}=\dfrac{\left(x-y\right)^2}{x^2-xy+y^2}.\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{x-y}=\left(x-y\right)\left(x+y\right)\)Vậy \(Q=\left(x-y\right)\left(x+y\right)\)