Thực hiện các phép tính sau: d) x+2/x^2+xy- y-2/xy+y^2 ;

Trả lời

d, $\frac{x+2}{x^2+xy}-\frac{y-2}{xy+y^2}$

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

$=\frac{\left(x+2\right)y}{xy\left(x+y\right)}-\frac{\left(y-2\right)x}{xy\left(x+y\right)}$

$=\frac{xy+2y-\left(xy-2x\right)}{xy\left(x+y\right)}$

$=\frac{xy+2y-xy+2x}{xy\left(x+y\right)}$

$=\frac{2y+2x}{xy\left(x+y\right)}=\frac{2\left(x+y\right)}{xy\left(x+y\right)}=\frac{2}{xy}$