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①已知x=2009,y=2010,求代数式x-y/x÷(x-(2xy-y^2/x))的值
②先化简,再求值:(a^2-b^2/a^2-ab)÷(a+(2ab+b^2/a)当b=-1时,再从-2<a<2的范围内选取一个合适的整数a代入求值
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人气:490 ℃ 时间:2020-04-13 12:08:36
解答
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①已知x=2009,y=2010,求代数式x-y/x÷(x-(2xy-y^2/x))的值
(x-y)/x÷[x-(2xy-y^2/x)]
=(x-y)/x÷(x²-2x+y²)/x
=(x-y)/x÷(x-y)²/x
=1/(x-y)
=1/(2009-2010)
=-1
②先化简,再求值:(a^2-b^2/a^2-ab)÷(a+(2ab+b^2/a)当b=-1时,再从-2<a<2的范围内选取一个合适的整数a代入求值
(a²-b²)/(a²-ab)÷[a+(2ab+b²/a)]
=[(a-b)(a+b)/a(a-b)]÷(a²+2ab+b²)/a
=(a+b)/a÷(a+b)²/a
=1/(a+b) b=-1 设a=0
=1/(0-1)
=-1
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