“先化简,再求值:(x+3分之x-3+x²-9分之6x)÷x²-9分之1,其中x=根号2009”小梁

[(x-3)/(x+3)]+6x/(x^2-9)]÷1/(x^2-9)=
=[(x-3)^2/(x+3)(x-3)+6x/(x^2-9)÷1/(x^2-9)
=[(x^2-6x+9+6x)/(x^2-9)]*(x^2-9)
=x^2+9
当x=-根号(2009)时,则
原式=[-根号(2009)]^2+9=[根号(2009)]^2+9=2009+9=2018
当x=-x时,则,(-x)^2=x^2
故,小粱虽写错了,但因x^2是偶数次方,其负值亦为正值,故结果也是正确的.