解方程(X-2)/(X+3)=1-(2X-13)/(X^2-9)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/09/01 16:40:14

解方程(X-2)/(X+3)=1-(2X-13)/(X^2-9)
(X+1)/(X-1)+ 4/(X^2-1)=1 1/(2-X)=1/(X-2) - (6-X)/(3X^2-12)

(X+1)/(X-1)+ 4/(X^2-1)=1 1/(2-X)=1/(X-2) - (6-X)/(3X^2-12)
[(X+1)^2+4]/(X^2-1)=1
X^2+2X+1+4=X^2-1
2X=-6
X=3
分式要检验
经检验,成立
1/(2-X)=1/(X-2) - (6-X)/(3X^2-12)
-1/(X-2)=1/(X-2) - (6-X)/[3(X+2)(X-2)]
-2/(X-2)=- (6-X)/[3(X+2)(X-2)]
2/(X-2)= (6-X)/[3(X+2)(X-2)]
6(X+2)(X-2)=(6-X)(X-2)
6X^2-24=-X^2+8X-12
7X^2-8X-12=0
X=2,X=-6/7
经检验,X=2是增根
X=-6/7

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