化简
（a/b-b/a)/(a+b/a)
=(a²-b²)/ab×a/(a+b)
=(a+b)(a-b)/ab×a/(a+b)
=(a-b)/b
(3x/x-1-x/x-1)*x^2-1/2x
=(3x-x)/(x-1)×(x+1)(x-1)/2x
=2x/(x-1)×(x+1)(x-1)/2x
=x+1
(x-3/x-1)/x^-9/x 前面2x应该为x吧
=(x-3)/(x-1)×x/(x+3)(x-3)
=x/[(x+3)(x-1)]
解方程
x/x+1=2x+1/x.
乘以x(x+1)得
x²=(2x+1)(x+1)
x²=2x²+3x+1
x²+3x+1=0
代入求根公式得
x=[-3±√(9-4)]/2
x1=(-3+√5)/2 x2=(-3-√5)/2
经检验,x1=(-3+√5)/2 x2=(-3-√5)/2 是原方程的解
3/2x-4-x/x-2=1/2
乘以2(x-2)得
3-2x=x-2
-2x-x=-2-3
-3x=-5
x=5/3
经检验,x=5/3是原方程的解