计算:X^2-Y^2/X^2+2XY+Y^2除以X+2Y/2X^2+2XY

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计算:X^2-Y^2/X^2+2XY+Y^2除以X+2Y/2X^2+2XY计算:X^2-Y^2/X^2+2XY+Y^2除以X+2Y/2X^2+2XY计算:X^2-Y^2/X^2+2XY+Y^2除以X+

计算:X^2-Y^2/X^2+2XY+Y^2除以X+2Y/2X^2+2XY
计算:X^2-Y^2/X^2+2XY+Y^2除以X+2Y/2X^2+2XY

计算:X^2-Y^2/X^2+2XY+Y^2除以X+2Y/2X^2+2XY
原式
=(x+y)(x-y)/(x+y)² × 2x(x+y)/(x+2y)
=(x-y)/(x+y) × 2x(x+y)/(x+2y)
=2x(x-y)/(x+2y)
=(2x²-2xy)/(x+2y)

解
(x²-y²)/(x²+2xy+y²)÷(x+2y)/(2x²+2xy)
=(x-y)(x+y)/(x+y)²÷(x+2y)/2x(x+y)
=(x-y)/(x+y)×[2x(x+y)/(x+2y)]
=2x(x-y)/(x+2y)
=(2x²-4xy)/(x+2y)