Question

计算分式 要详细步骤

x²-4y² x+2y
---------- ÷ --------分数线
x²+2xy+y² x²+xy
x²-4y² x+2y
----------÷--------分数线
x²+2xy+y² x²+xy
(x+2y)(x-2y)x(x+y)
=----------------
(x+y)(x+y)(x+2y)
(x-y)x
=------
(x+y)
这样对了吗？？？

Answer 1

x²-4y² x+2y
---------- ÷ --------分数线
x²+2xy+y² x²+xy

=(x+2y)(x-2y) x（x+y)
--------------* -------------
(x+y)² x+2y

=(x-2y)x
---------
x+y

Answer 2

[(x^2-4y^2)/(x^+2xy+y^2)]/[(x+2y)/(x^2+xy)]
=[(x-2y)(x+2y)/(x+y)^2]/[(x+2y)/x(x+y)]
=(x-2y)(x+2y)/(x+y)^2*x(x+y)/(x+2y)
=(x-2y)(x+2y)/(x+y)*x/(x+2y)
=(x-2y)/(x+y)*x
=x(x-2y)/(x+y)