Question

5x+y^2 phần x^2y -5y-x^2 phần xy^2

Answer 1

\(\dfrac{5x+y^2}{x^2y}-\dfrac{5y+x^2}{xy^2}\)

\(=\dfrac{y\left(5x+y^2\right)}{x^2y^2}-\dfrac{x\left(5y-x^2\right)}{x^2y^2}\)

\(=\dfrac{5xy+y^3}{x^2y^2}-\dfrac{5xy+x^3}{x^2y^2}\)

\(=\dfrac{5xy+y^3-5xy+x^3}{x^2y^2}\)

\(=\dfrac{\left(5xy-5xy\right)+x^3+y^3}{x^2y^2}\)

\(=\dfrac{x^3+y^3}{x^2y^2}\)

Answer 2

\(\dfrac{5x+y^2}{x^2y}-\dfrac{5y-x^2}{xy^2}=\dfrac{y\left(5x+y^2\right)}{y\cdot x^2y}-\dfrac{x\left(5y-x^2\right)}{x\cdot xy^2}\)

\(=\dfrac{5xy+y^3-5xy+x^3}{x^2y^2}=\dfrac{x^3+y^3}{x^2y^2}\) \(\left(x,y\ne0\right)\)