2除以(X的平方加上X) 加上 3除以(X平方减X)=4除以(X平方-1) 解方程组

Question

如题所述

Answer 1

2/(x^2+x)+3/(x^2-x)=4/(x^2-1)
2/[x(x+1)]+3/[x(x-1)]=4/[(x+1)(x-1)]
为使方程有意义，则X≠0且X≠1且X≠-1
方程两边同时乘以x(x+1)(x-1),
得2（x-1）+3(x+1)=4x
2x-2+3x+3=4x
解得x=-1
所以本方程无解。

Answer 2

等式两边的底数化为(x-1)(x+1)x，就等于2(x-1)/(x-1)(x+1)x+3(x+1)/(x-1)(x+1)x=4x/(x-1)(x+1)x,分子相加减(x+1)/(x-1)(x+1)x=0,化简就等于(x-1)x=0,解出X1=1,X2=0.
一定不是先把分母化掉.

Answer 3

解：方程两边同时乘以x(x+1)(x-1），得
2（x-1）+3（X+1）=4X
5x+1=4x
x=-1
检验：当x=-1时，x(x+1)(x-1）=0
所以原分式方程无解。

Answer 4

2/(x^2+x)+3/(x^2-x)=4/(x^2-1)
2/[x(x+1)]+3/[x(x-1)]=4/[(x+1)(x-1)]
去分母
2(x-1)+3(x+1)=4x
去括号
2x-2+3x+3=4x
移项,合并同类项
x=-1