已知a的平方+2a-2011=0.求代数式【(a-2)/(a的平方+2a)-(a-1)/(a的平方+4a+4)】÷(a-4)/(a+2)
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已知a的平方+2a-2011=0.求代数式【(a-2)/(a的平方+2a)-(a-1)/(a的平方+4a+4)】÷(a-4)/(a+2)
已知a的平方+2a-2011=0.求代数式【(a-2)/(a的平方+2a)-(a-1)/(a的平方+4a+4)】÷(a-4)/(a+2)
已知a的平方+2a-2011=0.求代数式【(a-2)/(a的平方+2a)-(a-1)/(a的平方+4a+4)】÷(a-4)/(a+2)
[(a-2)/(a^2+2a)-(a-1)/(a^2+4a+4)]/[(a-4)/(a+2)]
=[(a-2)/a(a+2)-(a-1)/(a+2)^2)]/ [(a-4)/(a+2)]
= [(a-2)(a+2)/a(a+2)^2-a(a-1)/a(a+2)^2)]/[(a-4)/(a+2)]
=[(a-4)/a(a+2)^2)]/[(a-4)/(a+2)]
=(a+2)/a(a+2)^2
=1/a(a+2)
=1/(a^2+2a)
a^2+2a-2011=0
a^2+2a=2011
所以原式=1/2011
【(a-2)/(a的平方+2a)-(a-1)/(a的平方+4a+4)】=[(a-2)*(a+2)-(a-1)*a]/[(a+2)*(a+2)*a]=(a-4)/[a*(a+2)*(a+2)]
【(a-2)/(a的平方+2a)-(a-1)/(a的平方+4a+4)】÷(a-4)/(a+2)
=1/[a*(a+2)]=1/(a的平方+2a)=1/2011
原式=[(a-2)/(a²+2a)-(a-1)/(a²+4a+4)] * (a+2)/(a-4) 【外边的除法转换成乘法】
=(a-2)/(a²+2a) * (a+2)/(a-4) - (a-1)/(a²+4a+4)* (a+2)/(a-4) 【把先减后乘转化为先乘后减】
=(a-2)/[a(a+2)]* (a+2)/(a-4) -(a-1)...
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原式=[(a-2)/(a²+2a)-(a-1)/(a²+4a+4)] * (a+2)/(a-4) 【外边的除法转换成乘法】
=(a-2)/(a²+2a) * (a+2)/(a-4) - (a-1)/(a²+4a+4)* (a+2)/(a-4) 【把先减后乘转化为先乘后减】
=(a-2)/[a(a+2)]* (a+2)/(a-4) -(a-1)/(a+2)² * (a+2)/(a-4) 【提取因式,整理,进行约分】
=(a-2)/[a(a-4)]-(a-1)/[(a+2)(a-4)]
=1/(a-4) * [(a-2)/a - (a-1)/(a+2)] 【提取公因式】
=1/(a-4) * [(a-2)(a+2)-a(a-1)]/[a(a+2)] 【通分】
=1/(a-4) * (a-4)/[a(a+2)] 【化简后约分】
=1/(a²+2a)=1/2011
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