Question

Tìm phân thức M biết:

\(\frac{x+y}{x-y}\cdot M=\frac{x^2+2xy+y^2}{x^2+xy+y^2}\)

 

 

Answer 1

\(\frac{x+y}{x-y}.M=\frac{x^2+2xy+y^2}{x^2+xy+y^2}\)

\(\Leftrightarrow M=\frac{x^2+2xy+y^2}{x^2+xy+y^2}.\frac{x+y}{x-y}\)

\(\Leftrightarrow M=\frac{\left(x+y\right)^3}{x^3-y^3}\)

\(\Leftrightarrow M=\frac{x^3+3x^2y+3xy^2+y^3}{x^3-y^3}\)

Answer 2

Sửa:

\(pt\Leftrightarrow M=\frac{x^2+2xy+y^2}{x^2+xy+y^2}.\frac{x-y}{x+y}\)

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

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

\(\Leftrightarrow M=\frac{x^2-y^2}{x^2+xy+y^2}\)