题目
（2X-3Y)（3X-4Y）=0求(X平方-2XY)/(X+Y)(X-2Y)
提问时间：2020-07-25
答案
（2X-3Y)（3X-4Y）=0
若2X-3Y=0 则X=3Y/2 代入得
[(3Y/2)^2-2*(3Y/2)*Y]/(3Y/2+Y)(3Y/2-2Y)
=(9Y^2/4-3Y^2)/(5Y/2)(-Y/2)
=(-3Y^2/4)/(-5Y^2/4)
=3/5
若3X-4Y=0 则X=4Y/3 代入得
[(4Y/3)^2-2*(4Y/3)*Y]/(4Y/3+Y)(4Y/3-2Y)
=(16Y^2/9-8Y^2/3)/(7Y/3)(-2Y/3)
=(-8Y^2/9)/(-14Y^2/9)
=4/7
若2X-3Y=0 则X=3Y/2 代入得
[(3Y/2)^2-2*(3Y/2)*Y]/(3Y/2+Y)(3Y/2-2Y)
=(9Y^2/4-3Y^2)/(5Y/2)(-Y/2)
=(-3Y^2/4)/(-5Y^2/4)
=3/5
若3X-4Y=0 则X=4Y/3 代入得
[(4Y/3)^2-2*(4Y/3)*Y]/(4Y/3+Y)(4Y/3-2Y)
=(16Y^2/9-8Y^2/3)/(7Y/3)(-2Y/3)
=(-8Y^2/9)/(-14Y^2/9)
=4/7
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