解分式方程【x²+1/x+1】+【3(x+1)/x²+1】=4
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![解分式方程【x²+1/x+1】+【3(x+1)/x²+1】=4](/uploads/image/z/2095432-16-2.jpg?t=%E8%A7%A3%E5%88%86%E5%BC%8F%E6%96%B9%E7%A8%8B%E3%80%90x%26%23178%3B%2B1%2Fx%2B1%E3%80%91%2B%E3%80%903%28x%2B1%29%2Fx%26%23178%3B%2B1%E3%80%91%3D4)
解分式方程【x²+1/x+1】+【3(x+1)/x²+1】=4
解分式方程【x²+1/x+1】+【3(x+1)/x²+1】=4
解分式方程【x²+1/x+1】+【3(x+1)/x²+1】=4
令t=(x²+1)/(x+1)
则方程化为:t+3/t=4
即t²-4t+3=0
(t-1)(t-3)=0
t=1,3
t=1时,x²+1=x+1,得:x(x-1)=0,得:x=0,1
t=3时,x²+1=3x+3,得:x²-3x-2=0,得:x=(3±√17)/2
经检验,以上4个解都为原方程的解.