Question

Tìm phân thức A biết: x -y/x³+y³× A = x² -2xy+y²/x²-xy+y²; x không bằng +y ,- y

Answer 1

Ta có: 

\(\dfrac{x-y}{x^3+y^3}\cdot A=\dfrac{x^2-2xy+y^2}{x^2-xy+y^2}\left(x\ne\pm y\right)\)

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

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

\(\Leftrightarrow A\cdot\left(x-y\right)=\left(x+y\right)\left(x-y\right)^2\)

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

\(\Leftrightarrow A=\left(x+y\right)\left(x-y\right)\)

\(\Leftrightarrow A=x^2-y^2\)