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(6x+12)/(x+2)^-(x^-4)/(x-2)^+x^/x^-4=0化简求值
题目详情
(6x+12)/(x+2)^ - (x^-4)/(x-2)^ + x^/x^-4 =0
化简求值
化简求值
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答案和解析
(6x+12)/(x+2)^=6(x+2)/(x+2)^=6/(x+2)
(x^-4)/(x-2)^=(x-2)(x+2)/(x-2)^=(x+2)/(x-2)
所以,(6x+12)/(x+2)^ - (x^-4)/(x-2)^
=6/(x+2)-(x+2)/(x-2)
通分,=[6(x-2)-(x+2)^]/(x^-4)
=(6x-12-x^-4x-4)/(x^-4)
=(-x^+2x-16)/(x^-4)
所以,(-x^+2x-16)/(x^-4)+x^/(x^-4)=0
(2x-16)/(x^-4)=0
2x-16=0
x=8
(x^-4)/(x-2)^=(x-2)(x+2)/(x-2)^=(x+2)/(x-2)
所以,(6x+12)/(x+2)^ - (x^-4)/(x-2)^
=6/(x+2)-(x+2)/(x-2)
通分,=[6(x-2)-(x+2)^]/(x^-4)
=(6x-12-x^-4x-4)/(x^-4)
=(-x^+2x-16)/(x^-4)
所以,(-x^+2x-16)/(x^-4)+x^/(x^-4)=0
(2x-16)/(x^-4)=0
2x-16=0
x=8
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