已知3x2+xy-2y2=0,求(x+yx-y+4xyy2-x2)÷x2+2xy-3y2x2-9y2的值.-数学

题目简介

已知3x2+xy-2y2=0,求(x+yx-y+4xyy2-x2)÷x2+2xy-3y2x2-9y2的值.-数学

题目详情

已知3x2+xy-2y2=0,求(
x+y
x-y
+
4xy
y2-x2
x2+2xy-3y2
x2-9y2
的值.
题型:解答题难度:中档来源:不详

答案

原式=[
(x+y)2
(x-y)(x+y)
+class="stub"-4xy
(x-y)(x+y)
(x+3y)(x-3y)
(x+3y)(x-y)
=class="stub"x-3y
x+y

由已知得(3x-2y)(x+y)=0,
因为x+y≠0,所以3x-2y=0,即x=class="stub"2
3
y,
所以原式=class="stub"x-3y
x+y
=
class="stub"2
3
y-3y
class="stub"2
3
y+y
=
-class="stub"7
3
y
class="stub"5
3
y
=-class="stub"7
5

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