Question

simplifique: X/x-y-Y/x+y+2xy/x2-y2

Answer 1

$\frac{x}{x}-y-\frac{y}{x}+y+2x\frac{y}{x}\cdot \:2-y\cdot \:2=2y+\frac{x-y}{x}\\ \\ \frac{x}{x}-y-\frac{y}{x}+y+2x\frac{y}{x}\cdot \:2-y\cdot \:2\\ \\ =-y+y-2y-\frac{y}{x}+2\cdot \:2\cdot \frac{y}{x}x+\frac{x}{x}\\ \\ =-y+y-2y+\frac{x-y}{x}+2\cdot \:2\cdot \frac{y}{x}x\\ \\ =-2y+\frac{x-y}{x}+2\cdot \:2\cdot \frac{y}{x}x\\ \\ =-2y+\frac{x-y}{x}+4y\\ \\ =-2y+4y+\frac{x-y}{x}\\ \\ =2y+\frac{x-y}{x}$