若x=2007,y=2008,则(x+y)*(x的四次-y的四次)分之(x的平方+y的平方)

问题描述:

若x=2007,y=2008,则(x+y)*(x的四次-y的四次)分之(x的平方+y的平方)

对原式进行化简得到=1/(x-y)=-1

先进行简化,再代入即可:
原式=(x+y)*(x*x+y*y)/(x*x*x*x-y*y*y*y)
=(x+y)*(x*x+y*y)/((x*x+y*y)(x*x-y*y))
=(x+y)/(x*x-y*y)
=(x+y)/((x+y)*(x-y))
=1/(x-y)
=1/(2007-2008)
=-1