两道因式分解和化简求值题.
因式分解:(m+n)^2-(m-n)^2.
化简求值:〔(x^2-2x)/x-2〕÷x+(x^2-1)/(x^2-2x+1),其中
x=1/2.
注:“/”为分数线.
噢,抱歉.我漏掉了x-1是有加括号的.
人气:473 ℃ 时间:2020-06-21 20:10:45
解答
(m+n)^2-(m-n)^2
=m^2+2mn+n^2-(m^2-2mn+n^2)
=2mn+2mn
=4mn
((x^2-2x)/x-2〕÷x+(x^2-1)/(x^2-2x+1)
=(x-2-2)÷x+(x-1)(x+1)/(x-1)^2
=(x-4)÷x+(x+1)/(x-1)
因为x=1/2,带入公式得:
=2(1/2-4)+(1/2+1)/(1/2-1)
=(1-8)+(3/2)/(-1/2)
=-7-3
=-10
若X-2是有括号的:
[(x^2-2x)/(x-2〕]÷x+(x^2-1)/(x^2-2x+1)
=[x(x-2)/(x-2)]÷x+(x-1)(x+1)/(x-1)^2
=1+(x+1)/(x-1)
因为x=1/2,带入公式得:
=1+(1/2+1)/(1/2-1)
=1+(3/2)/(-1/2)
=1-3
=-2
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