解方程:x+1分之x - x分之3x+3 = 2

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解方程:x+1分之x - x分之3x+3 = 2

解方程:x+1分之x - x分之3x+3 = 2
解方程:x+1分之x - x分之3x+3 = 2

解方程:x+1分之x - x分之3x+3 = 2
两边乘以x(x+1)得
x²-3(x+1)²=2x(x+1)
x²-3x²-6x-3=2x²+2x
4x²+8x+3=0
(2x+1)(2x+3)=0
∴x=-1/2 x=-3/2
检验:x=-1/2 x=-3/2是方程的解

x/(x+1)-(3x+3)/x=2 两边同乘x(x+1)
x^2-(3x+3)(x+1)=2x(x+1)
x^2-3(x+1)^2=2x(x+1)
x^2-3(x^2+2x+1)=2x^2+2x
x^2-3x^2-6x-3=2x^2+2x
4x^2+8x+3=0
(2x+1)(2x+3)=0
x=-1/2 或 -3/2

x/(x+1) - (3x+3)/x =2
x^2 - (x+1)(3x+3) =2x(x+1)
(2x+3)(2x+1)=0
x=-3/2 ,或x=-1/2

X1= -3/2,X2=-1/2