已知X+3/X+2=1/根号3+根号2+1,求X-3/2X-4除以(5/X-2 -X-2)的值 10
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取倒数
(x+2)/(x+3)=√3+√2+1
(x+2)/(x+3)-1=√3+√2+1-1
(x+2-x-3)/(x+3)=√3+√2
-1/(x+3)=√3+√2
原式
=[(x-3)/2(x-2)]/[(5/(x-2)-(x+2)]
=[(x-3)/2(x-2)]/[(5/(x-2)-(x+2)(x-2)/(x-2)]
=[(x-3)/2(x-2)]/[(5-x²+4)/(x-2)]
=[(x-3)/2(x-2)]/[-(x+3)(x-3)/(x-2)]
=-1/[2(x+3)]
=[-1/(x+3)]/2
=(√3+√2)/2
(x+2)/(x+3)=√3+√2+1
(x+2)/(x+3)-1=√3+√2+1-1
(x+2-x-3)/(x+3)=√3+√2
-1/(x+3)=√3+√2
原式
=[(x-3)/2(x-2)]/[(5/(x-2)-(x+2)]
=[(x-3)/2(x-2)]/[(5/(x-2)-(x+2)(x-2)/(x-2)]
=[(x-3)/2(x-2)]/[(5-x²+4)/(x-2)]
=[(x-3)/2(x-2)]/[-(x+3)(x-3)/(x-2)]
=-1/[2(x+3)]
=[-1/(x+3)]/2
=(√3+√2)/2
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