求解方程(x+6)/(x-6)[(x-4)/(x+4)]^2+（x-6）/(x+6)[(x+9)/(x-9)]^2=2（x^2+36）/(x^2-36)怎么没人回答的？

Question

求解方程(x+6)/(x-6)[(x-4)/(x+4)]^2+（x-6）/(x+6)[(x+9)/(x-9)]^2=2（x^2+36）/(x^2-36)
怎么没人回答的？

Answer 1

解:方程可变形为(x+6)/(x-6)[(x-4)/(x+4)]^2-（x-6）/(x+6)[(x+9)/(x-9)]^2+2（x-6）/(x+6)[(x+9)/(x-9)]^2=2（x^2+36）/(x^2-36)继续变形可得（x-6）/(x+6)[(x+9)/(x-9)]^2=（x^2+36）/(x^2-36),{注(x+6)/(x-6)[(x-4)/(x+4)]^2-（x-6）/(x+6)[(x+9)/(x-9)]^2=0}进一步变形可得x(2x^2-18x+27)=0解得x=0,x=(9±3根号3)/2