X/(X+1)+(X+1)/(X-1)=(3X+5)/(X²-1)

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X/(X+1)+(X+1)/(X-1)=(3X+5)/(X²-1)X/(X+1)+(X+1)/(X-1)=(3X+5)/(X²-1)X/(X+1)+(X+1)/(X-1)=(3X+

X/(X+1)+(X+1)/(X-1)=(3X+5)/(X²-1)
X/(X+1)+(X+1)/(X-1)=(3X+5)/(X²-1)

X/(X+1)+(X+1)/(X-1)=(3X+5)/(X²-1)
x(x-1)+(x+1)²=3x+5
x²-x+x²+2x+1=3x+5
2x²-2x-4=0
x²-x-2=0
(x-2)(x+1)=0
x=2
x=-1
检验x=-1是增根
∴方程解是x=2

x²-x+x²+2x+1=3x+5
2x²-2x-4=0
x²-x-2=0
x=2 或者x=-1

X/(X+1)+(X+1)/(X-1)=(3X+5)/(X²-1)
（x²-x+x²+2x+1）/（x²-1）=(3X+5)/(X²-1)
所以 2x²+x+1=3x+5 且x²-1≠0
x²-x-2=0 且x≠±1 （x-2）（x+1）=0
解得x=2
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左边加起来
(x*(x-1)+(x+1)^2)/(x^2-1)=(3x+5)/(x^2-1)
下面约掉在整理下
x^2-x+x^2+2x+1=3x+5
2x^2-2x-4=0
x^2-x-2=0
(x-2)(x+1)=0
x=2或者-1

把左边两个数的分母都转换成(X²-1)即（x+1)(x-1)就可以了
x(x-1)/(X²-1)+（x+1)²/(X²-1)=(3X+5)/(X²-1)
x(x-1)+（x+1)²=(3X+5)
展开解之即可

两边同时乘以(X+1)(X-1)得
X(X-1)+(X+1)²=(3X+5)
X²-X+X²+2X+1=3X+5
2X²-2X-4=0
X²-X-2=0
(X-2)(X+1)=0
X=2或x=-1
当X=-1时，分母X+1=0无意义，为增根
所以方程的解为x=2

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