方程4/[[x+1]2-4]-8/[[x+1]2-16]-2/[[x+2]2-1]+2/[[x-2]2-1]-6/[[x-2]2-9]=4/5的解为x=

题目

方程4/[[x+1]2-4]-8/[[x+1]2-16]-2/[[x+2]2-1]+2/[[x-2]2-1]-6/[[x-2]2-9]=4/5的解为x=

答案

4/[[x+1]2-4]=4/(x-1)(x+3)=[(x+3)-(x-1)]/(x-1)(x+3)
=(x+3)/(x-1)(x+3)-(x-1)/(x-1)(x+3)
=1/(x-1)-1/(x+3)
8/[[x+1]2-16]=8/(x-3)(x+5)=[(x+5)-(x-3)]/(x-3)(x+5)
=(x+5)/(x-3)(x+5)-(x-3)/(x-3)(x+5)
=1/(x-3)-1/(x+5)
2/[[x+2]2-1]=2/(x+1)(x+3)=[(x+3)-(x+1)]/(x+1)(x+3)
=(x+3)/(x+1)(x+3)-(x+1)/(x+1)(x+3)
=1/(x+1)-1/(x+3)
2/[[x-2]2-1]=2/(x-3)(x-1)=[(x-1)-(x-3)]/(x-3)(x-1)
=(x-1)/(x-3)(x-1)-(x-3)/(x-3)(x-1)
=1/(x-3)-1/(x-1)
6/[[x-2]2-9]=6/(x-5)(x+1)=[(x+1)-(x-5)]/(x-5)(x+1)
=(x+1)/(x-5)(x+1)-(x-5)/(x-5)(x+1)
=1/(x-5)-1/(x+1)
方程左边=[1/(x-1)-1/(x+3)]-[1/(x-3)-1/(x+5)]
-[1/(x+1)-1/(x+3)]+[1/(x-3)-1/(x-1)]-[1/(x-5)-1/(x+1)]
=1/(x-1)-1/(x+3)-1/(x-3)+1/(x+5)-1/(x+1)+1/(x+3)
+1/(x-3)-1/(x-1)-1/(x-5)+1/(x+1)
=[1/(x-1)-1/(x-1)]+[1/(x+3)-1/(x+3)]+[1/(x-3)-1/(x-3)]
+[1/(x+1)-1/(x+1)]+1/(x+5)-1/(x-5)
=1/(x+5)-1/(x-5)
=[(x-5)-(x+5)]/(x+5)(x-5)
=-10/(x^2-25)
方程化为：-10/(x^2-25)=4/5
-12.5=x^2-25
x^2=12.5
x=±(5√2)/2