Question

rút gọn Q=\(\dfrac{x^2}{xy+y^2}+\dfrac{y^2}{xy-y^2}+\dfrac{x^2+y^2}{xy}\)

Answer 1

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

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

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

\(=\dfrac{x^4-x^3y+x^2y^2+xy^3+x^4-y^4}{xy\left(x^2-y^2\right)}\)

\(=\dfrac{2x^4-x^3y+x^2y^2+xy^3-y^4}{xy\left(x^2-y^2\right)}\)