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比较(x+2)(x+6)与(x+3)(x+5)的大小

发布时间:2019-09-17

原式左右调换一项,减去1/x+2,
将算式同时乘以(x+1)(x+6)(x+2)(x+5) 得到(x+2)²(x+6)(x+5)+(x+7)(x+1)(x+2)(x+5)=(x+3)(x+1)(x+6)(x+5)+(x+6)²(x+1)(x+2) 得到[(x+2)(x+5)][(x+2)(x+6)+(x+7)(x+1)]=[(x+1)(x+6...
得 1\(x+3)(x+4)+1\(x+4)(x+5)=(2x+8)\(x+2)(x+6)-1\(x+2)(x+3) 两边简化,x+x/2+1+x+x/7+6 = x+x/3+2+x+x/6+5 ==>x/2+x/7+7 = (x/3+x/6)+7 ==>x/7 = 0 ==>x=0。x+2分之x+1+x+7分之x+6=x+3分之x+2+x+6分之x+5 x+1/x+2 + x+6/x+7=x+2/x+3+ x+5/x+6 1-1/x+2 + 1- 1/x+7=1-1/x+3+ 1-1/x+6 1/x+2 + 1/x+7=1/x+3+ 1/x+6 (x+7+x+2)/(x+2)(x+7)=(x+6+x+3)/(x+3)(x+6) (2x+9)(x+2)(x+7)=(2x+9)(x+3)(x+6) 。移项,
等式不变,解:x+1/x+2+x+6/x+7=x+2/x+3+x+5/x+6 原式=x+2/x+2 - 1/x+2 + x+7/x+7 - 1/x+7=x+3/x+3 - 1/x+3 + x+6 /x+6 -1/x+6(就是把分子上加1,得 [(x+7)-(x+6)]/(...。得 (x+5)\(x+3)(x+4)(x+5)+(x+3)\(x+4)(x+5)(x+3)=(2x+8)(x+3)\(x+2)(x+6)(x+3)-(x+6)\(x+2)(x+3)(x+6) 2/(x+3)(x+5)=(2x+9)/(x+3)(x+6) 。1/(x+2)+1/(x+6)=1/(x+5)+1/(x+3) 1/(x+2)-1/(x+3)=1/(x+5)-1/(x+6) (x+3-x-2)/[(x+2)(x+3)]=(x+6-x-5)/[(x+5)(x+6)] 1/[(x+2)(x+3)]=1/[(x+5)(x+6)] 1/(x^2+5x+6)=1/(x^2+11x+30) x^2+5x+6=x^2+11x+30 6x=-24 x=-4 经检验x=-4是方程的解。得 1/(x+6)-1/(x+7)=1/(x+2)-1/(x+3) 方程两边同时通分,(X+1/X+2)-(X+2/X+3)=(X+5/X+6)-(X+6/X+7) (X方+4X+3-X方-4X-4)/(X方+5X+6)=(X方+12X+35-X方-12X-36)/(X方+13X+42) X方+5X+6=X方+13X+42 -8X=36 X=-9/2。x+6/x+7+x+1/x+2=x+2/x+3+x+5/x+6 解:[(x+7)-1]/(x+7)+[(x+2)-1]/(x+2)=[(x+3)-1]/(x+3)+[(x+6)-1]/(x+6) 即:1-1/(x+7)+1-1/(x+2)=1-1/(x+3)+1-1/(x+6) 化简,变成类似x+2/x+2=1,得下步) =1- 1/x+2 + 1 - 1/x+7=1- 1/x+3 + 1- 1/x+6(把1约掉。(x+1)/(x+2)+(x+6)/(x+7)=(x+2)/(x+3)+(x+5)/(x+6) 1-1/(x+2)+1-1/(x+7)=1-1/(x+3)+1-1/(x+6) -1/(x+2)-1/(x+7)=-1/(x+3)-1/(x+6) 1/(x+2)+1/(x+7)=1/(x+3)+1/(x+6) 1/(x+2)-1/(x+3)=1/(x+6)-1/(x+7) 。作差法:(x+2)(x+6)-(x+3)(x+5)=(x
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