灵鹊做题网巧题妙解题 1/m+5-1/m+6=1/m+7-1/m+8
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巧题妙解题 1/m+5-1/m+6=1/m+7-1/m+8
1/(m+5)-1/(m+6)=1/(m+7)-1/(m+8)
(m+6)/[(m+5)(m+6)]-(m+5)/[(m+5)(m+6)]=(m+8)/[(m+7)(m+8)]-(m+7)/[(m+7)(m+8)]
[(m+6)-(m+5)]/[(m+5)(m+6)]=[(m+8)-(m+7)]/[(m+7)(m+8)]
1/[(m+5)(m+6)]=1/[(m+7)(m+8)]
(m+5)(m+6)=(m+7)(m+8)
m²+11m+30=m²+15m+56
11m-15m=56-30
-4m=26
m=-6.5
经检验m=-6.5是原方程的根
(m+6)/[(m+5)(m+6)]-(m+5)/[(m+5)(m+6)]=(m+8)/[(m+7)(m+8)]-(m+7)/[(m+7)(m+8)]
[(m+6)-(m+5)]/[(m+5)(m+6)]=[(m+8)-(m+7)]/[(m+7)(m+8)]
1/[(m+5)(m+6)]=1/[(m+7)(m+8)]
(m+5)(m+6)=(m+7)(m+8)
m²+11m+30=m²+15m+56
11m-15m=56-30
-4m=26
m=-6.5
经检验m=-6.5是原方程的根
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