1/(x^2+2x+10)+1/(x^2+11x+10)+1/(x^2-13x+10)=0

1/(x²+2x+10)+1/(x²+11x+10)+1/(x²-13x+10)=0
去分母
(x²+11x+10)(x²-13x+10)+(x²+2x+10)(x²-13x+10)+(x²+2x+10)(x²+11x+10)=0
整理,得x⁴-29x²+100=0
x⁴-25x²-4x²+100=0
x²(x²-25)-4(x²-25)=0
(x²-25)(x²-4)=0
(x+5)(x-5)(x+2)(x-2)=0
x=5或x=-5或x=2或x=-2,代入分式方程检验,分母均不等于0,4个解均为分式方程的解.
x=5或x=-5或x=2或x=-2