已知,x-4/x=2倍根号3 求代数式 [(2x²+10x)/(x²+4x+4)]/[(x+1)-12/(x+2)]的值

化简原式
=2x(x+5)／(x+2)²／[(x+1)-12/(x+2)]
=[2x(x+5)／(x+2)²]／﹛[(x+1)×(x+2)-12]／(x+2)﹜
=[2x(x+5)／(x+2)²]／[﹙x²+3x-10)／(x+2)]
=[2x(x+5)／(x+2)²]／[(x+5﹚×(x-2﹚／(x+2)]
=[2x(x+5)／(x+2)²]×﹛(x+2)／[(x+5﹚×(x-2﹚]﹜
=2x／[(x+2)×(x-2﹚]
=2x／﹙x²-4x﹚
由已知x-4/x=2√3可知x²-4x=2√3x
∴2x／﹙x²-4x﹚
=2x/2√3x
=1/√3
=√3/3