Question

Rút gọn phân thức:

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

Answer 1

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

Answer 2

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

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